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,19,0,0,0,0,0,Heath, T.L.,,,Diophantus of Alexandria, A study in the History of Greek Algebra,,,?,,1910,59,66,,1,,

,19,0,0,0,0,0,Houzeau de Lehaie, J.Cl.,,,Fragments sur le Calcul numérique,Bull. Acad. Belgique,40,,,1875,455,524,,1,,

,13,29,0,0,0,0,Luroth, J.,,,Vorlesungen über numersichen Rechnen.,,,?,,1900,0,0,,1,,

,19,0,0,0,0,0,Tannery, J.,,,Leçons d'Algèbre et d'Analyse,,,?,,1906,0,0,,1,,

,29,0,0,0,0,0,Hayashi, T.,,,The Bakhshali Manuscript.,,,E. Forsten,Groningen,1995,0,0,,1,0,

,19,0,0,0,0,0,Biernatzki, K.L.,,,Die Arithmetik der Chinesen,J. Reine Angew. Math.,52,,,1856,84,87,,1,0,

,19,0,0,0,0,0,Bortolotti, E.,,,La scuola matematica di Bologna,,,Cenno storico,Bologna,1928,0,0,,1,0,

,13,19,0,0,0,0,Bosmans, H.,,,La Théorie des équations dans L' "Invention Nouvelle en l'Algèbre d'Albert Giraud",Mathesis,40,,,1926,59,155,Deals with quadratics and cubics.,1,0,

,19,0,0,0,0,0,Anbouba, A.,,,L'algèbre arabe aux IXe et Xe siecles. Aperçu general.,J. Hist. Arabic Science,2,,,1978,66,100,,1,0,

,10,19,25,0,0,0,Berzolari, L.,,,Enciclopedia Italiana, Vol.2 on Algebra.,,,,Roma,1929,0,0,,1,0,

,19,0,0,0,0,0,Taton, R.,,,A General History of the Sciences. Vol. 1. Ancient and Medieval Science.,,,,Paris,1957,0,0,,1,0,

,19,0,0,0,0,0,Gandz, S.,,,The Algebra of Inheritance…,Osiris,5,,,1938,319,391,,1,0,

,19,0,0,0,0,0,Sarton, G.,,,Introduction to the History of Science,,,,Baltimore,1953,493,0,,1,0,

,13,0,0,0,0,0,Colerus, E.,,,De Pythagore à Hilbert,,,,Paris,1947,98,0,Historical survey (popular).,1,0,

,0,0,0,0,0,0,Wang, Z.,Han, D.,,On dominating sequence method in the point estimate and Smale theorem.,Science in China (Ser. A),33,,,1990,135,144,Smale proved:- Let α^ψ(α)² = q < 1 where ψ(r) = 2r²-4r+1, and α is an expression in the derivatives of f. Then Newton's iteration converges with order 2. We improve on this theorem.,1,0,

,15,0,0,0,0,0,Wang, Z.,Han, D.,Zheng, S.,Convergence on Euler's series: Euler's and Halley's iteration from data at one point,Acta Math. Sinica,33,,,1990,721,738,,1,0,

,3,15,0,0,0,0,Petkovic, M.S.,,,Halley-like Method with Corrections for the Inclusion of Polynomial Zeros,Computing,62,,,1999,69,88,Halley-type iterations for simultaneous inclusion of all zeros with convergence anlaysis for total-step method.,1,0,

,2,16,0,0,0,0,Shub, M.,,,On the work of Steve Smale on the theory of computation, in "From topology to Computation", Ed. M. Hirsch.,,,Springer-Verlag,New York,1993,281,301,Considers complexity of Newton's method.,1,0,

,2,0,0,0,0,0,Smale, S.,,,Newton's method estimates from data at one point, in "The Merging of Disciplines: New Directions in Pure, Applied and Computational Mathematics", Ed. R. Ewing et al.,,,Springer-Verlag,New York,1986,185,196,Gives conditions for z₀ to be an approximate zero of f(z) = 0, I.e. Newton's method converges rapidly to a root from z₀.,1,0,

,3,0,0,0,0,0,Neff, C.,,,Specified Precision Root Finding is in NC,J. Comput. System Sci.,48,,,1994,429,463,Given a polynomial of degree n with integer coefficients bounded by 2ⁿ, let us seek all roots with error < 2^{-μ}. A parallel algorithm is given of time O(log³(n+m+μ)).,1,0,

,1,0,0,0,0,0,Novak, E.,,,Determining zeros of increasing Lipschitz functions,Aequationes Math.,41,,,1991,161,167,Sukharev's variation of the Bisection algorithm is optimal on average.,1,0,

,10,17,0,0,0,0,Burgisser, P.,Clausen, M.,Shokrollahi, M.A.,Algebraic Computational Complexity.,,,Springer-Verlag,Berlin,1997,0,0,Sections on Greatest Common Divisors and evaluation of polynomials that are hard to compute,1,0,

,10,0,0,0,0,0,Collins, G.E.,Johnson, J.R.,Kuchlin, W.,Parallel real roots isolation using the coefficient sign variation method, in "Computer Algebra and Parallelism", Ed. R.E. Zippel,,,Springer-Verlag,New York,1992,71,87,Uses Descartes' rule of signs to search for isolation intervals. Checks initial interval, then bisects and searches left and right subintervals recursively in parallel.,1,0,

,19,0,0,0,0,0,Bradley C.,,,Integer roots of cubic equations.,Math. Gaz.,88,,,2004,508,511,Finds conditions for cubic with integer coefficients to have integer roots.,1,0,

,2,3,0,0,0,0,Sun, F.,Li, X.,,On an accelerating quasi-Newton circular iteration.,Appl. Math. Comput.,106,,,1999,17,29,Describes a parallel iteration in interval arithmetic and investigates its convergence, which is cubic with effectively 4 function evaluations,1,0,

,10,0,0,0,0,0,Cauchy, A.,,,Sur le dénombrement des racines qui, dans une équation algébrique ou transcendente, satisfont àdes conditions données,C.R. Acad. Sci. Paris,40,,,1855,1329,1335,,1,0,

,20,29,0,0,0,0,Cipolla, M.,,,Sulla risoluzione apiristica delle congruenze binomie secondo un modulo primo.,Math. Ann.,63,,,1906,54,61,

Solutions of $x^{n}$ ≡a (mod p)

,1,0,

,20,29,0,0,0,0,Cipolla, M.,,,Formole di risoluzione della congruenza binomia quadratica e biquadratica,Rend. Accad. Sci. Fis. Mat. Napoli,11,,,1905,13,18,

Solutions of $z^{2}$ ≡q (mod p)

,1,0,

,3,0,0,0,0,0,Petkovic M.,Petkovic L.,Ilic S.,The Guaranteed Convergence of Laguerre-Like Method,Comput. Math. Appl.,46,,,2003,239,251,Gives initial conditions which guarantee convergence of a fourth-order simultaneous method.,1,0,

,10,0,0,0,0,0,Brioschi, M.F.,,,Sur les fonctions de Sturm,C.R. Acad. Sci. Paris,68,,,1869,1318,1321,,1,0,

,17,0,0,0,0,0,Linnainmaa, S.,,,Taylor expansions of the accumulated rounding error,BIT,16,,,1976,146,160,Treats errors in Horner's method for evaluating a polynomial,1,0,

,28,0,0,0,0,0,Aihara,Y.,,,On some inequalities among the roots of an equation and its successive derivatives.,Proc. Phys.-Math. Soc. Japan Ser. 3,16,,,1934,1,6,Let F be an expression involving sums of powers of roots of f and its first 2 derivatives. We show that F may be 0, positive or negative according to the position of the roots.,1,0,

,20,0,0,0,0,0,Sims, C.C.,,,Abstract Algebra, A Computational Approach,,,Wiley,New York,1984,0,0,Section on factorization over finite fields.,1,0,

,13,0,0,0,0,0,Fateman, R.J.,,,Symbolic and Algebraic Computer Programming Systems,SIGSAM Bull.,15,1,,,1981,21,32,Macsyma can factorize certain simple high-degree polynomials such as xⁿ ±1.,1,0,

,22,0,0,0,0,0,Akritas, A.G.,,,There is no "Uspensky's method", in Proc. 1986 Symp. On Symbolic and Algebraic Computation, Ed. B.W. Char,,,ACM,New York,1986,88,90,We correct the misconception that there exists a method by Uspensky (based on Vincent's theorem) for the isolation of real roots of a polynomial with rational coefficients.,1,0,

,17,0,0,0,0,0,Overill, R.E.,Wilson, S.,,Performance of parallel algorithms for the evaluation of power series.,Parallel Comput.,20,,,1994,1205,1213,,1,0,

,20,0,0,0,0,0,Vandiver, H.S.,,,An Algorithm for the Solution of the Linear Congruence,Amer. Math. Monthly,31,,,1924,137,140,,1,0,

,10,20,0,0,0,0,Winkler, F.,,,Computer Algebra, in "The Encyclopedia of Physical Science and Technology", Ed. R.A. Meyers,,,Academic Press,,1986,0,0,Discusses polynomial remainder siquences for GCD's and Modular GCD algorithms For integral polynomials. Also factorization over finite fields, and Uspensky's algorithm for real roots.,1,0,

,2,0,0,0,0,0,Bergweiler, W.,,,Iteration of meromorphic functions.,Bull. Amer. Math. Soc. (N.S.),29,,,1993,151,188,Considers Julia sets, etc., including Newton's method,1,0,

,2,0,0,0,0,0,, P.,,,The dynamics of Newton's method, in "Complex Dynamical Systems, The mathmatics behind the Mandelbrot and Julia sets, Eds. R.L. Devaney et al,,,Amer. Math. Soc.,Providence,1994,139,154,,1,0,

,27,0,0,0,0,0,Bleher, P.,Di, X.,,Correlations between zeros of a random polynomial,J. Stat. Physics,88,,,1997,269,305,Obtains exact analytic expressions for correlation between real zeros of Kac random polynomials. Zeros in (-1,1) are independent of zeros outside this interval.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,On the average number of real roots of a random algebraic equation with dependent coefficients.,J. Indian Math. Soc.,50,,,1986,49,58,When coefficients are dependent with constant correlation the number of real roots is half that when they are independent.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Random polynomials with complex coefficients.,Statist. Probab. Lett.,27,,,1996,347,355,Estimates number of zeros of polynomials with independent random complex coefficients.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Sharp crossings of a non-staionary stochastic process and its application to random polynomials.,Stochastic Anal. Appl.,14,,,1996,89,100,Gives expected number of zeros with slope > u or < -u. This is asymptotically equal to total number of zeros (for fixed u).,1,0,

,27,0,0,0,0,0,Logan, B.F.,Shepp, L.A.,,Real zeros of random polynomials II.,Proc. London Math. Soc.,18,,,1968,308,314,Number of real zeros of a polynomial with normally distributed coefficients has expectation c log n where c depends on the parameter of the distribution.,1,0,

,27,0,0,0,0,0,Miroshin, R.N.,,,Mean number of real zeros of a Gaussian random polynomial with dependent coefficients.,Vestnik Leningrad Univ.,24,1,,,1991,48,55,number of real zeros is a complicated function of correlation coefficient.,1,0,

,27,0,0,0,0,0,Offord, A,C,,,,Lacunary entire functions,Math. Proc. Cambridge Philos. Soc.,114,,,1993,67,83,Lacunary entire functions, like random ones, are large except in very small neighbourhoods of their zeros.,1,0,

,27,0,0,0,0,0,Nayak, N.N.,Mohanty, S.P.,,On the lower bound of the number of real zeros of a random algebraic polynomial.,J. Indian Math. Soc.,49,,,1985,7,15,Gives lower bound for number of zeros when coefficients are dependent random variables.,1,0,

,20,0,0,0,0,0,Kaltofen, E.,Shoup, V.,,Fast polynomial factorization over high algebraic extensions of finite fields, in "ISSAC 97. Proc. 1997 Internat. Symp. Symbolic Algebraic Comput.", Ed. W. Kuchlin,,,ACM Press,New York,1997,184,188,

New algorithms factor polynomials of degree n

over field of q elements, where log q = $n^{1 + a},$

$in time O (n^{3 + a + o (1)} + n^{2.69 + 1.69 a})$

,1,0,

,20,0,0,0,0,0,Caris, P.A.,,,A solution of the quadratic congruence modulo p, p = 8n+1, n odd,Amer. Math. Monthly,32,,,1925,294,297,,1,0,

,21,0,0,0,0,0,Zarzo, A.,Dehesa, J.S.,,Spectral Properties of solutions of hypergeometric-type differential equations.,J. Comput. Appl. Math.,50,,,1994,613,623,Gives distribution of zeros of hypergeometric-type functions including classical orthogonal polynomials.,1,0,

,13,0,0,0,0,0,Giventhal, A.B.,,,Manifolds of polynomials having a root of a fixed comultiplicity and the general Newton equation.,Functional Anal. Appl.,16,,,1982,10,14,,1,0,

,13,0,0,0,0,0,Hilbert, D.,,,über die Gleichung neunten Grades.,Math. Ann.,97,,,1927,243,250,,1,0,

,22,0,0,0,0,0,Akritas, A.G.,,,Reflections on a pair of theorems by Budan and Fourier.,Math. Mag.,55,5,,,1982,292,298,The theorems considered lead to a method of isolating real roots (Vincent's), which is claimed to be more efficient than Sturm's method.,1,0,

,22,0,0,0,0,0,Akritas, A.G.,,,A remark on the proposed Syllabus for an AMS short course on Computer Algebra.,SIGSAM Bull.,14,2,,,1980,24,25,There is no Uspensky's method; credit should go to Vincent.,1,0,

,21,0,0,0,0,0,Arriola, E.R.,Zarzo, A.,Dehesa, J.S.,Spectral properties of the biconfluent Heun differential equation,J. Comput. Appl. Math.,37,,,1991,161,169,Gives number of zeros per unit interval of n'th degree Heun polynomials,1,0,

,22,0,0,0,0,0,Akritas, A.G.,Ng, K.H.,,Exact algorithms for polynomial real roots approximation using continued fractions.,Computing,30,,,1983,63,76,Uses infinite precision to solve integer-coefficient polynomial to any required accuracy. Based on Vincent's theorem.,1,0,

,2,12,0,0,0,0,Alefeld, G.,Potra, F.A.,Völker, W.,Effective improvements of the interval-Newton-method, in "Scientific Computing and Validated Numerics", Ed. G. Alefeld et al,,,Akademie-Verlag,Berlin,1996,133,139,Gives methods similar to Interval-Secant and Super-Secant of efficiency up to 1.839. In practise they are not much better than Interval-Newton.,1,0,

,29,0,0,0,0,0,Lang, T.,Montuschi, P.,,Higher Radix Square Root with Prescaling,IEEE Trans. Comput,41,,,1992,996,1009,Prescale to a value close to 1, use a radix-256 one-digit per iteration approach. Hardware oriented.,1,0,

,2,4,7,10,19,20,Bieberbach, L.,Bauer, G.,,Vorlesungen über Algebra,,,Teubner,Leipzig,1933,0,0,Existence, Congruences, Classical Numerical Methods.,1,0,

,2,16,0,0,0,0,Smale, S.,,,Some remarks on the foundations of numerical analysis.,SIAM Rev.,32,,,1990,211,220,Complexity considered briefly.,1,0,

,18,21,0,0,0,0,Van Doorn, E.A.,,,Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tre-diagonal matrices.,J. Approx. Theory,51,,,1987,254,266,,1,0,

,20,0,0,0,0,0,Lord, N.,,,Prime values of polynomials.,Math. Gaz.,79,,,1995,572,573,If p is degree n and is prime for 2n+1 integer values, then p is irreducible.,1,0,

,20,21,0,0,0,0,Gonchar, A.A.,Rakhmanov, E.A.,,Equilibrium measure and distribution of the zeros of extremal polynomials.,Math. USSR Sb.,53,,,1986,119,130,,1,0,

,20,21,0,0,0,0,Rakhmanov, E.A.,,,Equilibrium measure and the distribution of zeros of extremal polynomials of a discrete variable.,Math. Sb.,187,,,1996,1213,1228,,1,0,

,13,0,0,0,0,0,Noether,,,James Joseph Sylvester,Math. Ann.,50,,,1898,138,146,,1,0,

,2,10,0,0,0,0,Moigno,,,Théorèmes de Descartes, de Rolle, de budan et Fourier, de M.M. Sturm et Cauchy.,Nouv. Ann. Math.,3,,,1844,188,194,,1,0,

,20,0,0,0,0,0,Bianchi, L,,,Lezioni sulla Teoria dei Numeri algebrici.,,,Zanichelli,Bologna,1923,87,0,Decomposition into irreducible factors; congruences mod p.,1,0,

,20,0,0,0,0,0,Kaltofen, E.,Shoup, V.,,Subquadratic-Time factoring of Polynomials over Finite Fields, in "Proc. 27th Ann. ACM. Symp. On the Theory of Computing",,,ACM Press,,1995,398,406,New probablistic algorithms are presented for factoring polynomials over finite fields in time of order n to the power 1.815. They rely on fast matrix multiplication techniques.,1,0,

,13,0,0,0,0,0,Furstenau, E.,,,Neue Methode zur Darstellung und Berechnung der imaginaren Wurzeln algebraischer Gleichungen durch Determinanten der Coefficienten,Schrift. Ges. Bef. Ges. Naturwiss. Marburg,9,,,1871,19,48,,1,0,

,3,0,0,0,0,0,Kirrinnis, P.,,,Fast Numerical Improvement of Factors of Polynomials and of Partial Fractions, in "Proc. 1998 Intern. Symp. On Symbolic and Algebraic Computation", Ed. O. Gloor,,,ACM Press,,1998,260,267,Uses multidimensional Newton iteration applied to the coefficient vectors. Provides starting value conditions and time bounds.,1,0,

,13,0,0,0,0,0,McNamee, J.M.,,,An updated supplementary bibliography on roots of polynomials.,J. Comput. Appl. Math.,110,,,1999,305,306,Covers the period roughly 1993-1999, plus many earlier ones. On Web.,1,0,

,10,0,0,0,0,0,Chin, P.,Corless, R.M.,Corliss, G.F.,Optimization Strategies for the Approximate GCD Problem, in "Proc. 1998 Intern. Symp. On Symbolic and Algebraic Computation-ISSAC98", Ed. O. Gloor,,,ACM Press,,1998,228,235,,1,0,

,27,0,0,0,0,0,Odoni, R.W.K.,,,Zeros of random polynomials over a finite field.,Math. Proc. Cambridge. Philos. Soc.,111,,,1992,193,197,,1,0,

,27,0,0,0,0,0,Panda, R.K.,Pratihari, D.,Pattanaik, B.P.,On the number of real roots of a random algebraic equation.,J. Austral. Math. Soc. (Ser. A),54,,,1993,86,96,,1,0,

,27,0,0,0,0,0,Pratihari, D.,Pattanaik, B.P.,,On the lower bound of the number of real roots of random algebraic equations.,Bull. Inst. Math. Acad. Sinica,19,,,1991,251,260,,1,0,

,27,0,0,0,0,0,Sambandham, M.,,,On the average number of real zeros of a class of random algebraic curves.,Pacific J. Math.,81,,,1979,207,215,Gives upper bound on number of real roots where coefficients are dependent.,1,0,

,11,0,0,0,0,0,Soh C.B.,,,Generalization of the Hermite-Behler Theorem and application,IEEE Trans. Automat. Control,35(2),,,1990,222,225,,1,0,

,27,0,0,0,0,0,Samal, G.,Mishra, M.N.,,Real zeros of a random algebraic polynomial.,Quart. J. Math. Oxford,24,,,1973,169,175,Gives lower bound for number of real roots for polynomial whose coefficents have specified range of variance and third moment.,1,0,

,27,0,0,0,0,0,Samal, G.,Mishra, M.N.,,On the upper bound of the number of real roots of a random algebraic equation with infinite variance II.,Proc. Amer. Math. Soc.,44,,,1974,446,448,450,1,0,

,27,0,0,0,0,0,Uno, T.,,,On the lower bound of the number of real roots of a random algebraic equation,Statist. Probab. Lett.,30,,,1996,157,163,The coefficients are dependent Gaussian random variables.,1,0,

,27,0,0,0,0,0,Shenker, M.,,,The mean number of real roots for one class of random polynomials.,Ann. Probab.,9,,,1981,510,512,For low correlation between random Gaussian coefficients, the number of roots is the same as if correlation were zero.,1,0,

,13,0,0,0,0,0,Bellavitis, G.,,,Risoluzione numerica delle equazioni.,Mem. Reale Ist. Veneto Sci. Let. Arti,6,,,1857,357,413,,1,0,,p> ,0,21,0,0,0,0,Kuijlaars, A.B.J.,Rakhmanov, E.A.,,corr. To "Zero distributions to discrete orthogonal polynomials" (JCAM 99 255),J. Comput. Appl. Math.,104,,,1999,213,213,Theorem 7.1 of original paper is incorrect.,1,0,

,15,0,0,0,0,0,Drakopoulos, V.,Argyropoulos,N.,Bohm, A.,Generalized computation of Schröder iteration functions to motivate families of Julia and Mandelbrot-like sets.,SIAM J. Numer. Anal.,36,,,1999,417,435,Gives a new algorithm to generate the Schröder functions and maximize their efficiency, Describes Julia sets related to a particular cubic.,1,0,

,21,0,0,0,0,0,He, M.,,,The faber polynomials for circular arcs, in "The mathematics of Computation 1943-1993". Ed. W. Gautschi,,,Amer. Math. Soc.,Providence, RI,1995,301,304,let E be a set, and w = Φ(z) be a conformal mapping of C\E to exterior of circle |w| = PE. Then with certain conditions Φ(z) = z + a₀+a₁/z+.. F_n = polynomial part of {Φ(z)}ⁿ, is Faber polynomial of degree n generated by E. Studies Faber polynomials associated with a circular arc, as well as zeros of these polynomials.,1,0,

,1,2,10,14,0,0,Reverchon, A.,Ducamp, ??,,Mathematical Software Tools in C++,,,Wiley,,1993,0,0,Treats Bisection, Newton's and Bairstow's methods. Also greatest common divisors.,1,0,

,13,0,0,0,0,0,Schnuse, C.H.,,,Die theorie und Auflösung der höheren algebraischen und der transcendente Gleichungen.,,,Braunschweig,,1850,0,0,,1,0,,p> ,15,0,0,0,0,0,Yao, Q.,,,On Halley Iteration,Numer. Math.,81,,,1999,647,677,We exhibit the non-overshoot property (will not skip over m zeros) of halley's iteration and also its monotonic convergence to real roots.,1,0,

,1,2,7,0,0,0,Woodford, C.,Phillips, C.,,Numerical Methods with Worked Examples,,,Chapman & Hall,,1997,0,0,treats Bisection, Newton and Secant methods,1,0,

,19,25,0,0,0,0,Varadarajan, V.S.,,,Algebra in Ancient and Modern Times,,,Amer. Math. Soc.,Providence, RI,1998,0,0,Treats cubic and biquadratic equations (Cardano etc) and fundamental theorem of algebra,1,0,

,2,10,13,0,0,0,Torii, T.,Sakurai, T.,Suguira, H.,An Application of Sunzi's Theorem for Solving Algebraic Equations, in "Proc. First China-Japan Seminar on Numerical Mathematics", Ed. Z.-C. Shi and T. Ushijama,,,World Scientific,Singapore,1993,155,167,Method based on Newton, Sturm sequences, etc.,1,0,

,15,0,0,0,0,0,Wang, X.H.,Han, D.,,The Global Convergence of a Family of Iterations, in "Proc. First China-Japan Seminar on Numerical Mathematics", Ed. Z.-C. Shi and T. Ushijama,,,World Scientific,Singapore,1993,230,233,Methods based on high-order derivatives.,1,0,

,29,0,0,0,0,0,Werthum,,,Die Arithmetik des Elia Misrachi,,,,,1849,0,0,Treats square and cube roots,1,0,

,10,0,0,0,0,0,Hattensdorffs, K.,,,Die Sturmschen Funktionen,,,,Hannover,1874,0,0,Describes Sturm's theorem and related matters,1,0,

,10,0,0,0,0,0,Balinski, A.I.,Podlevski, B.M.,,Computaional Aspects of the Application of Frobenius Matrix to Separation of Roots of Polynomials,Comput. Math. Math. Phys.,39,,,1999,1029,1033,Considers Bezoutian matrix (resultant) of two polynomials, and conditions that they have common roots.,1,0,

,19,0,0,0,0,0,Zhi, L.,Liu, Z.,,P-Irreducibility of Binding Polynomials,Computers Math. Applic.,38 2,,,1999,1,10,Gives conditions, for degree 3 and 4, that a polynomial with positive coefficients can be factored (or not) into polynomials with same property.,1,0,

,1,2,7,14,15,17,Schwarz, H.R.,,,Numerical Analysis: A Comprehensive Introduction,,,Wiley,Chichester,1989,0,0,Standard text-book treatment of Bisection, Newton, Secant, Evaluation, Muller.,1,0,

,10,0,0,0,0,0,Locher, F.,Skrzipek, M.-R.,,A stability test for complex polynomials,Analysis,15,,,1995,205,219,Uses argument principle and Sturm sequences to find the number of zeros inside the unit circle or the unimodular zeros.,1,0,

,20,0,0,0,0,0,Itoh, T.,,,An Efficient Probabilistic Algorithm for Solving Quadratic Equation over Finite Fields,Electron. Commun. Japan (part 3),72,3,,,1989,88,96,Proposes a probabilistic algorithm in which the probability that the desired solution is obtained by one application is kept as one-half and the quadratic equation is solved more efficiently than by Rabin's method.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Random Polynomials,Appl. Math. Lett.,3,2,,,1990,43,46,The behaviour of an algebraic and a trigonometric polynomial is reviewed, and the number of times that the curve representing these polynomials cross any real line in the xy-plane is presented.,1,0,

,5,12,0,0,0,0,Schaeffer, M.J.,,,Precise Zeros of Analytic Functions Using Interval Mathematics,Interval Computations,4,,,1993,22,39,An interval arithmetic algorithm for the computation of zeros of an analytic function inside a rectangle is presented. It is based on the argument principle, is guaranteed to converge, and has a specified accuracy.,1,0,

,17,0,0,0,0,0,Pan, V.Y.,et al,,Fast multipoint polynomial evaluation and interpolation via computations with structured matrices,Ann. Numer. Math.,4,,,1997,483,510,Considers multipoint polynomial evaluation via FFT. Extended to Chebyshev representation.,1,0,

,20,29,0,0,0,0,Cipolla, M.,,,Sulla risoluzione aparistica delle congruenze binomie,Atti. R. Accad. . Lincei Rend. Ser. 5,16,,,1907,603,608,

Solves $z^{n}$ ≡a (mod p)

,1,0,

,20,29,0,0,0,0,Capelli, A,,,Sulla riduttibilita della funcione $x^{n}$ -A in un campo qualunque.,Math. Ann.,54,,,1901,602,603,,1,0,

,17,0,0,0,0,0,Reif, J.H.,,,Approximate complex polynomial evaluation in near constant work per point, in "Proc. 29th Annual ACM Symp. On Theory of Computing".,,,ACM Press,New York,1997,30,39,

Let k = log(|P|/ε) where |P| = Σ| $a_{i} |; ϵ = bound on evaluation error . We evaluate P at m≥nlogn / \log^{2} k$

$points in O (\log^{2} logn) work per point . For special points used in signal processing$

$the work is even less .$

,1,0,

,19,0,0,0,0,0,Rose, P.,,,The Italian Renaisssance of Mathematics,,,Librarie Droz,Geneva,1975,0,0,Treats early solution of cubic and quartic (Cardan, Tartaglia, etc),1,0,

,20,0,0,0,0,0,Manove, M.,Bloom, S.,Engelman, C.,Rational functions in MATLAB, in "Symbolic Manipulation Languages and Techniques", Ed. D.G. Bobrow,,,North Holland,Amsterdam,1968,86,102,Deals with factorization of polynomials with integer coefficients into polynomials irreducible over the integers.,1,0,

,3,0,0,0,0,0,Petkovic, M.S.,Ilic, S.,,Point estimation and the convergence of the Ehrlich-Aberth method,Publ. Inst. Math.,62,,,1997,141,149,Considers the Ehrlich-Aberth method for simultaneous approximation of simple zeros, and initial conditions which enable safe convergence.,1,0,

,20,0,0,0,0,0,Pohst, M.,Zassenhaus, H.,,Algorithmic Algebraic Number Theory,,,Cambridge Univ. Press,London,1989,69,86,Considers factorizing polynomial over finite field into irreducible factors.,1,0,

,2,0,0,0,0,0,Kirrinnis, P.,,,Newton Iteration Towards a Cluster of Polynomial Zeros, in "Foundations of Computational Mathematics", Ed. F. Cucker and M. Shub.,,,Springer-Verlag,New York,1997,193,215,Coefficient of factor corresponding to a roots cluster are computed using Newton iteration in C to the power k. The starting value condition is very restrictive.,1,0,

,29,0,0,0,0,0,Ashenhurst, R.L.,,,Function evaluation in unnormalized arithmetic.,J. Assoc. Comput. Mach.,11,,,1964,168,187,Section on square root.,1,0,

,20,29,0,0,0,0,Fitch, J.,,,A Simple Method of Taking nth Roots of Integers,SIGSAM Bull.,8,no. 4,,,1974,26,26,Uses Newton's method, where only interested in case where root is itself an integer,1,0,

,20,0,0,0,0,0,Schwartz, S.,,,Contribution à la réductibilité des polynômes dans la théorie des congruences.,Ceska Spol. Nauk. Trida Mat.-Pri. Vest. Prague,,,,1939,1,7,,1,0,

,3,0,0,0,0,0,Petkovic, M.,Herceg, D.,,Borsch-Supan-like methods:Point estimation and parallel implementation.,Internat. J. Comput. Math.,64,,,1997,327,341,Gives initial condition for convergence of Borsch-Supan method and its Weierstrass modification for simultaneous approximation of zeros. Compares the methods on parallel computers.,1,0,

,20,0,0,0,0,0,Gianni, P.,Trager, B.,,Square-free Algorithms in Positive Charactersitic,Applic. Alg. Eng. Comm. Comput.,7,,,1996,1,14,We study the problem of the computation of the square-free decomposition for polynomials over fields of positive characteristic.,1,0,

,20,25,0,0,0,0,Mines, R.,Richman, F.,Ruitenberg, W.,A Course in Constructive Algebra,,,Springer-Verlag,Berlin,1988,0,0,Treats factorization into irreducible factors and fundamental theorem.,1,0,

,25,0,0,0,0,0,Frohlich, A.,Sheperdson, J.C.,,Effective Procedures in Field Theory,Philos. Trans. Roy. Soc. London Ser. A,248,,,1956,407,432,Treats existence of splitting algorithms.,1,0,

,13,19,0,0,0,0,De. Morgan,,,Budget of Paradoxes,,,,,1872,292,375,Treats Horner's method,1,0,

,10,19,0,0,0,0,Perkins, G.R.,,,Treatise on Algebra,,,,New York,1842,0,0,,1,0,

,27,0,0,0,0,0,Hirata, H.,,,Macro-Properties of Real Roots of a Random Algebraic Equation,J. Fac. Eng. Chiba Univ.,38,,,1980,35,42,The distribution of the real roots of a random algebraic equation, whose coefficients are dependent normal random variables with arbitrary mean, covariance and variance, are studied.,1,0,

,21,0,0,0,0,0,Gilewicz, J.,Leopold, E.,,Location of the zeros of polynomials satisfying three-term recurrence relations with complex coefficients,Integral Trans. Spec. Functions,2,,,1994,267,278,The method leads to the exact interval where all zeros of classical polynomials are located.,1,0,

,19,0,0,0,0,0,Lewy, H.,,,Studies in assyro-babylonian mathematics and Metrology,Orientalia,18,,,1949,40,67,,1,0,

,2,15,19,0,0,0,Nordgaard, M.A.,,,A historical survey of algebraic methods of approximating the roots of numerical higher equations up to the year 1819.,,,Teachers College,,Columbia Univ., NY,1922,0,0,Covers early history of methods such as Regula Falsi, Vieta's, Newton-Raphson, Halley, Horner's,1,0,

,1,2,17,0,0,0,Dorn, W.,McCracken, D.,,Numerical Methods with FORTRAN IV Case Studies,,,Wiley,New York,1972,0,0,Considers Newton, Bisection, Successive Approximation, and Horner's method.,1,0,

,19,0,0,0,0,0,Sayyid Taha Baqir,,,Old Babylonian problem texts found in Tell Harmal,Sumer,6,,,1950,130,148,Gave solution to quadratic (probably the earliest).,1,0,

,29,0,0,0,0,0,Sachs, A.,,,Babylonian Mathematical Texts II-III,J. Cunieform Studies,6,,,1952,151,156,Babylonians gave method for cube root.,1,0,

,19,0,0,0,0,0,Miller G.A.,,,The Oldest Extant mathematics,School & Society,35,,,1932,833,834,Babylonians had formula similar to modern ones for roots of a quadratic.,1,0,

,29,0,0,0,0,0,Darboux, G.,,,Sur l'extraction de la racine carré,Bull. Sci. Math. Ser. 2,11,,,1887,176,184,Square roots.,1,0,

,28,0,0,0,0,0,Ahmad, M,,,On polynomials with real zeros,Canad. Math. Bull.,11,,,1968,237,240,Considers roots of a polynomial and its derivative.,1,0,

,21,0,0,0,0,0,Dilcher, K.,Nulton, J.D.,Stolarsky, K.B.,The zeros of a certain family of trinomials,Glasgow Math. J.,34,,,1992,55,74,GET THIS,1,0,

,28,0,0,0,0,0,Meir, A.,Sharma, A.,,On zeros of derivatives of polynomials.,Canad. Math. Bull.,11,,,1968,443,445,GET THIS,1,0,

,18,28,0,0,0,0,Sz.-Nagy, B.,,,über algebraische Gleichungen mit lauter reellen Wurzeln.,Jahresber. Deutsch. Math.-Verein.,27,,,1918,37,43,,1,0,

,27,21,0,0,0,0,Das, M.,,,Real zeros of a random sum of orthogonal polynomials,Proc. Amer. Math. Soc.,27,,,1971,147,153,

Let $P_{k}^{*} (x) be normalized Legendre polynomials, then average number of zeros$

$c_{0} P_{0}^{*} + . . . + c_{n} P_{n}^{*} in [- 1,1] is asymptotically \frac{n}{\sqrt{3}}, for large n .$ ,1,0,

,21,27,0,0,0,0,Das, M.,Bhatt, S.S.,,Real roots of random harmonic equations,Indian J. Pure Appl. Math.,13,,,1982,411,420,

Let $ϕ_{k} (k = 0, . ., n) be a sequence of classical orthogonal polynomials, and c_{0}, . . . c_{n}$

be independent normal random variables, and $a_{0}, . . ., a_{n} normalizing constants in a certain sense . The expectation of real zeros of$

Σ $c_{k} a_{k} ϕ_{k} = \frac{n}{\sqrt{3}} as n \to \infty .$

,1,0,

,22,0,0,0,0,0,Chen, J.,,,A new algorithm for the isolation of the real roots of polynomial equations, in "Second Intern. Conf. On computers and Applications",,,,Beijing, China,1987,714,719,Isolates multiple real roots of polynomials with integer coefficients. Uses Vincent's theorem and continued fractions. Time O(n³L³(|p₀|)) where L(integer) = Log(abs(integer)), |p₀|=largest coefficient of polynomial.,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,On the average number of crossings of an algebraic polynomial,Indian J. Pure Appl. Math.,20,,,1989,1,9,

If P(x) = $Σ_{0}^{n - 1} a_{i} x^{i}, where the a_{i}$ are standard normal random variables, and $\frac{m^{2}}{n}$ →0 as

n→∞, the expectation of the number of real roots of P(x) = mx ∼ $\frac{1}{π} \log ($ n/ $m^{2}) if$

m tends to infinity with n or approaches( log n)/π if m bounded.

,1,0,

,21,27,0,0,0,0,Farahmand, K.,,,Level crossings of a random orthogonal polynomial.,Analysis,16,,,1996,245,253,

Gives asymptotic estimate of number of K-level crossings of a random combination of Legendre polynomials.The number → $\frac{n}{\sqrt{3}}$ provided ( $K^{2} / n)$ → 0 as n → ∞,1,0,

,25,0,0,0,0,0,Loria,,,Sur une démonstration du théorème fondamental de la théorie des équations algébriques.,Acta Math.,9,,,1886,71,0,An article by Holst in the preceding year is very similar to one by Mourey in 1828 (concerning existence of solutions).,1,0,

,25,0,0,0,0,0,Cauchy, A.L.,,,Sur les racines imaginaires des équations.,J. Ecole Poly.,18,,,1820,411,416,,1,0,

,25,0,0,0,0,0,Burg, A.,,,Ueber die Existenz der Wurzeln einer höhern Gleichung mit einer Unbekannten.,J. Reine Angew. Math.,5,,,1830,182,184,186,1,0,

,27,0,0,0,0,0,Glendinning, R.,,,The growth of the expected number of real zeros of a random polynomial.,J. Austral. Math. Soc. (Ser. A),46,,,1989,100,121,Let X₀,…,X_n be a stationary Gaussian process. We give conditions for expected number of real zeros of ΣX_jz^j to be (2 log n)/π as n → ∞,1,0,,p> ,27,0,0,0,0,0,Glendinning, R.,,,The growth of the expected number of real zeros of a random polynomial with dependent coefficients.,Math. Proc. Cambridge Philos. Soc.,104,,,1988,547,559,If coefficients form a stationary uniformly mixing sequence, then expected number of real zeros in [0,1] ∼ (logn)/(2π). As n → ∞,1,0,

,27,0,0,0,0,0,Samal, G.,Mishra, M.N.,,On the upper bound of the number of real roots of a random algebraic equation with infinite variance.,J. London Math. Soc.,6,,,1973,598,604,Number usually ≤ μ(log n)²,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Crossing of a random algebraic polynomial.,Indian J. Pure Appl. Math.,21(2),,,1990,109,115,,1,0,

,27,0,0,0,0,0,Farahmand, K,,,Exceedence measure of random polynomials.,Indian J. Pure Appl. Math.,26(9),,,1995,897,907,,1,0,

,19,0,0,0,0,0,Needham, Joseph,,,Science and Civilization in China,,III,Cambridge Univ Press,,1954,0,0,,1,0,

,2,0,0,0,0,0,von Haeseler, F.,Peitgen, H.O.,,Newton's method and complex dynamical systems,Acta Appl. Math.,13,,,1988,3,58,Considers Basins of attraction for Newton's method, including a historical survey, & reference to Julia and Mandelbrot sets. Also in "Newton's Method and Dynamical Systems", ed. H.O. Peitgen, Kluwer, Dordrecht, (1989),1,0,

,2,0,0,0,0,0,Hurley, M.,,,Multiple Attractors in Newton's Method,Ergodic Theory Dynamical Systems,6,,,1986,561,569,If d>=2, exists a polynomial of degree d so that its Newton function has 2d-2 periodic attractors.,1,0,

,18,0,0,0,0,0,Sylvester,J. J.,,,"Algebraical Researches containing a disquisition on Newton's Rule for the Discovery of Imaginary Roots,…,Philos.Trans. Roy. Soc. London,154,,,1864,579,666,Gives lower bound to number of imaginary roots of equation up to 5th degree, etc.,1,0,

,18,0,0,0,0,0,Sylvester, J.J.,,,"On the explicit values of Sturm's Quotients",Phil. Mag. Ser. 4,6,,,1853,293,296,,1,0,

,17,0,0,0,0,0,Miklosko, J.,,,Complexity of Parallel Algorithms in "Algorithms, Software and Hardware of Parallel Computers", eds. J. Miklosko and V.E. Kotov,,,Springer,Berlin,1984,47,48,Gives parallel algorithm for evaluating a polynomial,1,0,

,25,0,0,0,0,0,Bishop, E.,,,Foundations of constructive analysis,,,McGraw-Hill,,1967,0,0,Proves Fundamental Theorem,1,0,

,29,0,0,0,0,0,Ch'u-chung, Ting,,,Pai-fu-t'ang Mathematical Collections,,,,,1876,0,0,,1,0,

,13,0,0,0,0,0,Aki-ko, Taira,,,Sampo Shojo or Maiden's Arithmetic,,,,Japan,1774,0,0,,1,0,

,0,20,0,0,0,0,Dirichlet-Dedekind,,,Zahlentheorie,,,,,1968,,,Considers quadratic congruences,1,0,

,7,0,0,0,0,0,Coreless, R.M.,,,Cofactor iteration,SIGSAM Bull.,30(1),,,1996,34,38,Finds GCD of approximately known pair of polynomials.,1,0,

,10,0,0,0,0,0,Emiris, I.Z.,Galligo, A.,Lombardi, H.,Certified approximate univariate GCD's.,J. Pure and Applied Algebra,117-8,,,1997,229,251,Uses SVD,1,0,

,10,0,0,0,0,0,Karmarkar, N.,Lakshman, Y.N.,,Approximate polynomial greatest common divisors and nearest singular polynomials in Proc. Internat. Symp. On Symbolic and Algebraic Comput. (ISSAC),Y.N. Lakshman ed.,,,ACM Press,New York,1996,35,39,,1,0,

,25,0,0,0,0,0,Laisant, C.A.,,,Démonstration nouvelle du théorème fondamental de la théorie des équations,Bull. Soc. Math. France,15,,,1887,42,44,Fundamental Theorem of Algebra,1,0,

,29,0,0,0,0,0,Breuer, S.,Zwas, G.,,Numerical Mathematics- a Laboratory Approach,,,Cambridge Univ. Press,,1993,0,0,An excellent treatment of square and cube roots, including third order methods based on Halley etc.,1,0,

,20,0,0,0,0,0,Roelse, P.,,,Factoring high-degree polynomials over F₂ with Niederreiter's algorithm on the IBM SP2,Math. Comp.,68,,,1999,869,880,Involves setting up and solving a system of linear equations, which is performed in parallel. A new record is set.,1,0,

,19,29,0,0,0,0,Labat, R.,,,La Mesopotamie,,,Press Univ. de France,,1957,113,114,Babylonians found $\sqrt{2}$ to 6D, and solved quadratics.,1,0,

,7,0,0,0,0,0,Zou, X,,,Analysis of the quasi-Laguerre method,Numer. Math.,82,,,1999,491,519,Variation of Laguerre's method without using second derivatives. Order 1+ $\sqrt{2}$ . In some cases convergence guaranteed.,1,0,

,10,0,0,0,0,0,Krandick, W.,,,Isolierung reeler Nullstellen von Polynomen, in "Wissenschaftliches Rechnen", ed. J. Herzberger,,,Akademie Verlag,Berlin,1905,105,154,Uses Descartes' rule,1,0,

,10,20,0,0,0,0,Lipson, J.D.,,,Elements of Algebraic Computing,,,Addison-Wesley,,1981,0,0,Treats Root-finding over Power Series Domains,1,0,

,19,0,0,0,0,0,Van Der Waerden, B.L.,,,Science Awakening,,,,Groningen,1954,,0,Cubics among Babylonians,1,0,

,27,0,0,0,0,0,Leadbetter, M.R.,,,On Crossing of levels and curves by a wide class of stochastic processes.,Ann. Math.Statist.,37,,,1966,260,267,Shows that tangencies have probability 0.,1,0,

,27,0,0,0,0,0,Leadbetter, M.R.,Cryer, J.D.,,The variance of the number of zeros of a stationary normal process.,Bull. Amer. Math. Soc.,71,,,1965,561,563,,1,0,

,27,0,0,0,0,0,Ylvisaker, N.D.,,,The expected number of real zeros of a stationary Gaussian process..,Ann. Math.Statist.,36,,,1965,1043,1046,,1,0,

,29,19,0,0,0,0,Datta, B.,Singh, A.N.,,History of Hindu mathematics, I and II,,,Asia Publishing House,,1962,0,0,Deals with square and cube roots, quadratic equations,1,0,

,29,0,0,0,0,0,Kaye, G.R.,,,Indian Mathematics,Isis,2,,,1919,327,356,Square roots.,1,0,

,19,29,0,0,0,0,Kaye, G.R.,,,The Bakshali Manuscript: A Study in Medieval Mathematics.,,43,Aditya Prakashan,New Delhi,2004,0,0,Quadratics & Square roots,1,0,

,19,2,0,0,0,0,Burton, D.M.,,,The History of Mathematics, an Introduction,,,Allyn & Bacon,Boston,1986,0,0,Treats cubics & quadratics Cardan etc.,1,0,

,19,0,0,0,0,0,Heath, T.L.,,,The Thirteen Books of Euclid's Elements,,,Cambridge Univ. Press,,1926,0,0,Gives geometric solution of quadratics.,1,0,

,28,0,0,0,0,0,Cayley, A.,,,Sur les Racines D'une Équation Algébrique,C.R. Acad. Sci. Paris,110,,,1890,174,176,Show that if f'(x)=0 has n-1 roots, then f(x)=0 has n.,1,0,

,28,0,0,0,0,0,Meir, A.,Sharma, A.,,Span of derivatives of polynomials,Amer. Math. Monthly,74,,,1967,527,531,Let σ(p) = max real root-min real root, where roots all real. Proves that, if roots also positive, their sum ≤1/n, and k≤n-2, then max(σ(p^(k)))=n-k. Also a similar result for Σx_i²≤1/n.,1,0,

,22,0,0,0,0,0,Akritas, A.G.,,,A Short Note on a New Method for Polynomial Real Root Isolation.,SIGSAM Bull.,12(4),,,1978,12,13,Based on Vincent's method for isolating real roots by continued fractions. Order of n⁵,1,0,

,21,27,0,0,0,0,Das, M.,,,Real zeros of a random sum of orthogonal polynomials.,Proc. Amer. Math. Soc.,27,,,1971,147,153,Let c_i be random variables with expectation zero and variance 1, P_k^* be Legendre polynomials, then Σ₀ⁿP_k^* has average number of zeros ∼ n/ $\sqrt{3}$ ,1,0,

,27,0,0,0,0,0,Mishra, M.N.,Nayak, N.N.,Pattanayak,S.,Strong results for real zeros of random polynomials,Pacific J. Math,103,,,1982,509,522,,1,0,

,29,0,0,0,0,0,Ayyangar,,,The Bakhshali Manuscript,Mathematics Student,7,,Madras, India,1939,1,16,Treats square roots.,1,0,

,13,0,0,0,0,0,Rolle, M.,,,Demonstratio d'une Méthode pour Résoudre les Égalites de toutes Degrez,,,,,1691,0,0,,1,0,

,13,0,0,0,0,0,Delagny,,,Analyse Générale,,,,Paris,1733,0,0,,1,0,

,19,0,0,0,0,0,Cardan, G.,,,Arithmetic,,,,,1550,0,0,Section on square and cube roots,1,0,

,13,0,0,0,0,0,Legebeke, G.J.,,,Eene Eigenschap van de Wortels Eener Afgeleide Vergelijking,Nieuw Archief Voor Wiskunde (Ser. 1),8,,,1881,75,80,,1,0,

,29,0,0,0,0,0,Gupta, R.C.,,,Baudhayana's Value of $\sqrt{2}$ ,Mathematics Education,6,,,1972,77,79,Gives ancient derivation of $\sqrt{2}$ , accurate to 5D.,1,0,

,10,0,0,0,0,0,Cajori, F.,,,On Michel Rolle's book "Méthode pour résoudre les egalitez" and the history of "Rolle's theorem".,Bibl. Math. (Ser. 3),12,,,1911,300,313,Method similar to Sturm's sequences,1,0,

,13,0,0,0,0,0,Van Den Berg, F.J.,,,Over Het Verband Tusschen de Wortels Eener Vergelijking en die van Hare Afgeleide.,Nieuw Arch. Wisk. (Ser. 1),9,,,1882,1,14,,1,0,

,25,0,0,0,0,0,Macnie, J.,,,Proof of the theorem that every equation has a root,The Analyst,5,,,1878,80,82,,1,0,

,25,0,0,0,0,0,Mertens, F.,,,Der Fundamentalsatz der Algebra,Mon. Math. Phys.,3,,,1892,293,308,,1,0,

,1,2,7,10,0,0,Nonweiler, T.R.F.,,,Computational Mathematics-An Introduction to Numerical Approximation,,,Ellis Horwood,Chichester,1984,0,0,Standard treatment of Bisection, Newton, Secant, Sturm,1,0,

,16,0,0,0,0,0,Petkovic, M.S.,Petkovic, L.D.,,On bounds of the R-order of some iterative methods,Z. Angew. Math. Mech.,69 T,,,1989,197,198,,1,0,

,29,0,0,0,0,0,Channabasappa, M.N.,,,The Bakhshali Square-Root Formula and High-Speed Computation,Ganita Bharati,1,,,1979,25,27,It is more efficient than Newton's square-root method,1,0,

,20,0,0,0,0,0,Schwarz, St.,,,Contribution a la réductibilté des polynômes dans la théorie des congruences,Ceska Spol. Prague, Trida Math.-Prir. Vest.,,,,1939,1,7,Relates irreducible factors to a characteristic polynomial,1,0,

,3,5,0,0,0,0,Wang, X.,Xuan, X.,,Random Polynomial Space and Computational Complexity Theory,Sci. Sinica (Ser. A) Math. Phys. Astr. Tech. Sci.,30,,,1987,673,684,Recommends Lehmer's method with parallel disk iteration.,1,0,

,29,0,0,0,0,0,Enestrom, G.,,,Une note dans M. Cantor…,Bibl. Math. Ser. 3,8,,,0,412,413,Deals with cube roots,1,0,

,20,0,0,0,0,0,Maller, M.,Whitehead, J.,,Efficient p-adic Cell Decomposition for Univariate Polynomials,J. Complexity,15,,,1999,513,525,Finite fields,1,0,

,19,29,0,0,0,0,Elfering, K.,,,Die Mathematik des Aryabhata I,,,Wilhelm Fink Verlag,Munich,1975,0,0,Gives details of square and cube roots, and quadratic, as computed in early India.,1,0,

,2,0,0,0,0,0,Fouret, G.F.,,,Sur la Méthode d'approximation de Newton,Nouv. Ann. Math.,,,,1890,567,585,Treats Newton's method,1,0,

,19,0,0,0,0,0,Savasordo, A.,,,Liber embadorum,,,??,??,1145,0,0,Brought Arabic solution of quadratic to the West.,1,0,

,19,0,0,0,0,0,Pacioli, L.,,,Summa de Arithmetica Geometria Proportioni et Proportionalita,,,??,>>,1494,0,0,deals with quadratics,1,0,

,19,0,0,0,0,0,Stevin, S.,,,L'Arithmétique,,,,,1585,0,0,Reduces all quadratics to a single type,1,0,

,19,0,0,0,0,0,Stifel, M.,,,Die Coss,,,,,1524,0,0,Considers negative roots of quadratic,1,0,

,19,0,0,0,0,0,Stifel, M.,,,Arithmetica Integra,,,,,1544,0,0,quadratic,1,0,

,25,0,0,0,0,0,Enriques, F.,,,Questioni riguardanti le matematiche elementari Vol. I,,,,Bologna,1912,547,561,Considers fundamental theorem of algebra (existence of roots),1,0,

,25,0,0,0,0,0,Ko, K.,,,Complexity Theory of Real Functions,,,Birkhauser,Boston,1991,0,0,Section on existence and computability of roots of functions,1,0,

,28,0,0,0,0,0,Horwitz, A.,,,On the Ratio Vectors of Polynomials,J. Math. Anal. Appl.,205,,,1997,568,576,Relation between roots of a polynomial and its derivative, when the polynomial has all real roots,1,0,

,25,0,0,0,0,0,Sigrist,,,Equations of prime degree: Problem 88-4 by E. Galois,Math. Intelligencer,11,,,1989,53,54,proves that an equation of prime degree is solvable by radicals iff all its roots are rational functions of any 2 of them.,1,0,

,19,0,0,0,0,0,Patterson, W.M.,Lubecke, A.M.,,A special circle for quadratic equations.,Math. Teacher,84,,,1991,125,127,Gives graphical method for roots of quadratic.,1,0,

,19,0,0,0,0,0,Feser, V.G.,,,Special circle II.,Math. Teacher,85,,,1992,173,174,Gives history of a graphical method for a quadratic.,1,0,

,19,0,0,0,0,0,Pope, C.,,,Special circle I.,Math. Teacher,85,,,1992,173,0,Gives history of a graphical method for a quadratic.,1,0,

,19,0,0,0,0,0,Holmes, C.R.,,,Imagine the roots of a quadratic.,Math. Gaz.,74,,,1990,285,286,Way of "seeing" graphically the imaginary roots of a quadratic.,1,0,

,29,0,0,0,0,0,Brown, l.M.,,,An algorithm for square roots: an episode in the campaign against dotage.,Math. Gaz.,81,,,1997,428,0,Gives a new formula for square root.,1,0,

,29,0,0,0,0,0,Cortadella, J.,Lang, T.,,High-radix Division and Square Root with Speculation,IEEE Trans. Computers,43,,,1994,919,931,One digit produced per iteration,1,0,

,2,0,0,0,0,0,Ford, W.F.,Pennline, J.A.,,Accelerated convergence in Newton's method,SIAM Rev.,38,,,1996,658,659,Modifies Newton's method using N'th root of f', to achieve N'th order convergence,1,0,

,4,0,0,0,0,0,Willers, F.A.,,,Rechenkontrollen und Reschenschemata zum Graeffeschen Verfahren,Wiss. Zeit. Tech. Hochschule Dresden,2,,,1952,327,332,,1,0,

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,27,0,0,0,0,0,Wilkins, J.E.,,,The expected value of the number of real zeros of a random sum of Legendre polynomials.,Proc. Amer. Math. Soc.,125,,,1997,1531,1536,The expected number is n/ $\sqrt{3}$ +o(n^δ for any δ > 0.,1,0,

,20,0,0,0,0,0,Hurwitz, A.,,,Über höhere Kongruenzen,Arch. Math. Phys. (Ser. 3),5,,,1903,17,27,Considers a₁x^p-2+a₂x^p-3+…+a_p-1 ≡ 0 (mod p).,1,0,

,20,0,0,0,0,0,Kühne, H.,,,Bemurkungen zu der Abhandlung der herrn Hurwitz: Über höhere Kongruenzen.,Arch. Math. Phys. (Ser. 3),6,,,1904,174,0,see note on article by Hurwitz.,1,0,

,20,29,0,0,0,0,Mignosi, G.,,,La convergenza in un campo di integrita finito e la risoluzione apiristica dell congrunze binomie.,Rend. Circ. Mat. Palermo,50,,,1926,245,253,Considers e.g. x^{2^r}≡ a (mod 2^α),1,0,

,29,0,0,0,0,0,Knill, R.J.,,,A modified Babylonian algorithm.,Amer. Math. Monthly,99,,,1992,734,737,Algorithm for sqrt(x); z₁=1;a₁ = (x+1)/(x-1), z_k+1=z_k(1+1/a_k),a_k+1 = 2a_k²-1; then z_k → $\sqrt{x}$ from below.,1,0,

,29,0,0,0,0,0,Deslauriers, G.,Dubuc, S.,,Le calcul de la racine cubique selon Héron.,Elem. Math.,51,,,1996,28,34,If a and b are integers whose cubes enclose N, d₁ = N-a³, d₂ = b³-N, Heron takes a + bd₁(b-a)/(bd₁+ ad₂). We give error bounds for this and related formulas.,1,0,

,18,20,0,0,0,0,Boyd, D.W.,,,Speculations concerning the range of Mahler's measure,Canad. Math. Bull.,24,,,1981,453,469,Deals with Measure = |a₀| Π_I=1ⁿ max (|root_i|,1) of a polynomial with integer coefficients.,1,0,

,18,20,0,0,0,0,Mossinghoff, M.J.,,,Polynomials with small Mahler measure.,Math. Comp.,67,,,1998,1697,1705,Deals with Measure = |a₀| Π_I=1ⁿ max (|root_i|,1) of a polynomial with integer coefficients.,1,0,

,18,20,0,0,0,0,Rausch, U.,,,On a theorem of Dobrowolski about conjugate numbers.,Colloq. Math.,50,,,1985,137,142,Deals with Measure = |a₀| Π_I=1ⁿ max (|root_i|,1) of a polynomial with integer coefficients.,1,0,

,20,0,0,0,0,0,Blake, I.F.,Mullin, R.C.,,The Mathematical Theory of Coding.,,,Academic Press,New York,1975,0,0,Section on polynomials over finite fields.,1,0,

,20,0,0,0,0,0,Pless, V.,,,Introduction to the Theory of Error-Correcting Codes.,,,Wiley-Interscience,New York,1982,0,0,Considers factors of xⁿ-1 over finite field.,1,0,

,20,0,0,0,0,0,Tonelli, A.,,,Bemurkung über die Auflösung quadratischer Congruenzen.,Nachr. Akad. Wiss. Gottingen,,,,1891,344,346,Solves xⁿ = c(mod p).,1,0,

,27,0,0,0,0,0,Mallows, C.L.,Schilling, K.,,Random Polynomials with Real Roots.,Amer. Math. Monthly,106,,,1999,477,0,Fix ε > 0 and n ≥ 1, then a polynomial of degree n with random coefficients can be found which has n distinct real roots with probablity ≥ 1-ε,1,0,

,15,0,0,0,0,0,Kalantari, B,,,On the order of convergence of a determinantal family of root-finding methods.,BIT,39,,,1999,96,109,For a family B_m^k of iteration functions for roots, we show that for a fixed m, as k incrreases, the order decreases from m to the positive root of t^k-Σ₀^k-1t^j. Also for fixed k, the order increases with m.,1,0,

,20,29,0,0,0,0,Mathews, G.B.,,,Theory of Numbers,,,Chelsea,New York,1960,0,0,Treats congruences such as x² ≡ a (mod m).,1,0,

,1,2,14,15,0,0,Pozrikidis, C.,,,Numerical Computation in Science and Engineering,,,Oxford,,1998,0,0,Treats bisection, Bairstow and Newton's methods, Laguerre's method.,1,0,

,29,0,0,0,0,0,McBride, A.,,,Remarks on Pell's equation and square root algorithms,Math. Gaz.,83,,,1999,47,52,Newton's method for square roots is related to Pell's equation:- find positive integers u,v so that u²-av² = ± 1 ( a positive integer).,1,0,

,17,0,0,0,0,0,Revah, I.,,,On the number of Multiplications/Divisions Evaluating a Polynomial with Auxiliary Functions.,SIAM J. Comput.,4,,,1975,381,392,Shows that for n < 9, minimum number of mults/divides to evaluate a polynomial is (n+2)/2, while for n ≥ 9 it is almost always (n+1)/2.,1,0,

,17,0,0,0,0,0,Rabin, M.O.,Winograd, S.,,Fast Evaluation of Polynomials by Rational Preparation,Comm. Pure Appl. Math.,25,,,1972,433,458,Treats Pre-conditioning of polynomials by addition,subtraction and multiplication only. Gives an algorithm of order n/2 + O(log n) multiplies and n+o(n) adds. Also considers case where division allowed.,1,0,

,20,0,0,0,0,0,Skolem. T.,,,On a certain connection between the discriminant of a polynomial and the number of its irreducible factors mod p.,Norsk Mat. Tidskr.,34,,,1952,81,85,,1,0,

,25,0,0,0,0,0,Collins, E.,,,Neuer Beweis der Zerlegbarkeit ganzer Functionen in reelle Factoren vom ersten oder zweiten Grade.,J. Reine Angew. Math.,18,,,1838,119,126,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Liouville, J.,,,Sur le principe fondamental de la théorie des équations algébriques.,J. Math. Pure Appl.,4,,,1839,501,508,Treats existence of roots,1,0,

,25,0,0,0,0,0,Deahna, F.,,,Neuer Beweis für die Auflösbarkeit der algebraischen Gleichungen durch reelle oder imaginäre Werthe der Unbekannten.,J. Reine Angew. Math.,20,,,1840,337,339,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Stern,,,Elementarer Beweis eines Fundamentalsatzes aus der Theorie der Gleichungen.,J. Reine Angew. Math.,23,,,1842,370,371,Treats fundamental theorem of algebra.,1,0,

,25,0,0,0,0,0,Moret,,,Beweis der Satzes, dass jede algebraische ganze Function von einer Veränderlichen in Factoren vom ersten Grade aufgelöset werden kann.,J. Reine Angew. Math.,29,,,1845,97,102,Treats existence,1,0,

,25,0,0,0,0,0,Sussman, J.,,,Vereinfachung des Beweises von Cauchy, dass jede Gleichung n^ten Grades wenigstens eine Wurzel hat.,J. Reine Angew. Math.,44,,,1852,57,59,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Foscolo, G.,,,Sulla necessaria esistenza di una radice reale o imaginaria in ogni equazione algebrica.,Giorn. Mat.,2,,,1864,13,16,Treats existence.,1,0,

,25,0,0,0,0,0,Transon, A.,,,Démonstration de deux théorèmes d'algèbre.,Nouv. Ann. Math. (Ser.2),7,,,1868,97,110,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Clifford, W.K.,,,Proof that every rational equation has a root.,Proc. Cambridge Phil. Soc.,2,,,1870,156,157,Dividing an even degree polynomial by a quadratic,and eliminating the constant term of the quadratic, we eventually reach an odd degree polynomial, which is known to have a root.,1,0,

,25,0,0,0,0,0,Kinkelin, H.,,,Neuer Beweis des Vorhandenseins complexer Wurzeln in einer algebraischen Gleichung.,Math. Ann.,1,,,1870,502,506,Treats existence.,1,0,

,25,0,0,0,0,0,Walton, W.,,,A demonstration that every equation has a root.,Quart. J. Math.,11,,,1871,178,182,Uses Leibnitz' theorem.,1,0,

,25,0,0,0,0,0,Walton, W.,,,Démonstration du théorème de Cauchy: Toute équation a une racine.,Nouv. Ann. Math. (Ser. 2),10,,,1871,509,514,Treats existence.,1,0,

,25,0,0,0,0,0,Netto, E.,,,Beweis der Wurzelexistenz algebraischer Gleichungen.,J. Reine Angew. Math.,88,,,1880,16,21,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Walecki,,,Démonstration du théorème fondamental de la théorie des équations algébriques.,C.R. Acad Sci. Paris,96,,,1882,772,773,Treats existence of roots.,1,0,

,25,0,0,0,0,0,Dutordoir, H.,,,Toute équation algébrique a une racine; démonstration nouvelle.,Ann. Soc. Sci. Bruxelles,7,,,1883,,,Treats existence,1,0,

,25,0,0,0,0,0,Dutordoir, H.,,,Démonstration nouvelle du théorème fondamental de la théorie des équations algébriques.,C.R. Acad. Sci. Paris,97,,,1883,742,744,Treats existence.,1,0,

,25,0,0,0,0,0,Hocks, H.,,,Ueber den Fundamentalsatz der algebraischen Gleichungen.,Z. Math. Phys.,28,,,1883,123,125,Treats fundamental theorem of algebra.,1,0,

,25,0,0,0,0,0,Walecki,,,Démonstration du théorème de D'Alembert.,Nouv. Ann. Math. (Ser. 3),2,,,1883,241,248,Treats existence.,1,0,

,25,0,0,0,0,0,Fields, J.C.,,,A proof of the theorem: the equation f(z) = 0 has a root where f(z) is any holomorphic function of z.,Amer. J. Math.,8,,,1886,178,179,Proof in terms of minimum distance from origin, if never 0.,1,0,

,25,0,0,0,0,0,Holst, E.,,,Beweis des Satzes dass jede algebraische Gleichung eine Wurzel hat.,Acta. Math.,8,,,1886,155,160,Treats existence of root.,1,0,

,25,0,0,0,0,0,Perott, J.,,,Démonstration du théorème fondamental de l'algèbre.,J. Reine Angew. Math.,88,,,1886,141,146,Treats existence of roots.,1,0,

,25,0,0,0,0,0,von Dalgwick, F.,,,Ueber einen Beweis des Fundamentalsatzes der Algebra.,Z. Math. Phys.,34,,,1889,185,188,Treats existence.,1,0,

,25,0,0,0,0,0,Phragmén, E.,,,Ein elementarer Beweis des Fundamentalsatzes der Algebra.,Svenska Vet. Ofv. Forh.,48,,,1891,113,120,Treats fundamental theorem of algebra.,1,0,

,28,29,0,0,0,0,Brown, J.E.,Xiang G.,,Proof of the Sendov Conjecture for Polynomials of Degree at Most Eight,J. Math. Anal. Appls.,232,,,1999,272,292,If all the zeros of p lie in the unit disk, then it has a critical point within unit distance of each zero. Proved for degree ≤8 and arbitrary degree if at most 8 distinct zeros.,1,0,

,5,0,0,0,0,0,Kravanja, P.,Van Barel, M.,,A Derivative-Free Algorithm for Computing Zeros of Analytic Functions,Computing,63,,,1999,69,91,Gives an algorithm for computing all zeros inside a closed curve, by evaluating integrals along the curve.,1,0,

,2,0,0,0,0,0,Lang, T.,Montuschi, P.,,Very High Radix Square Root with Prescaling and Rounding and a Combined Division/Square Root Unit,IEEE Trans. Comps.,48,,,1999,827,841,Hardware oriented,1,0,

,19,0,0,0,0,0,Beran, L.,,,The complex roots of a quadratic from a circle,Math. Gaz.,83,,,1999,287,291,,1,0,

,25,0,0,0,0,0,Horng, G.,Huang, M.D.,,Solving polynomials by radicals with roots of unity in minimum depth,Math. Comp.,68,,,1999,881,885,Involves Galois groups, splitting fields, etc.,1,0,

,3,0,0,0,0,0,Iliev, A.I.,Semerdzhiev, Kh. I.,,Some Generalizations of the Chebyshev Method for Simultaneous Determination of All Roots of Polynomial Equations,Comput. Math. Math. Phys.,39,,,1999,1384,1391,The multiplicities are assumed known in advance. The methods have cubic order.,1,0,

,29,0,0,0,0,0,Rangacayra, M.,,,The Ganita-Sara-sangraha of Mahaviracarya,,,Madras Govt. Press,,1912,0,0,Considers square & cube root,1,0,

,29,0,0,0,0,0,Karp, A.H.,Markstein, P.,,High Precision Division and Square Root,ACM Trans. Math. Software,23,,,1997,561,589,,1,0,

,19,0,0,0,0,0,Bortolotti, E.,,,Studi i richerchi sulla storia della matematica in Italia nei secoli xvi e xvii,,,Zanichelli,Bologna,1828,0,0,History of solution of low-order polynomials,1,0,

,20,0,0,0,0,0,Buchberger B. et al,,,Rechnerorientierte Verfahren,,,B.G. Teubner,Stuttgart,1986,0,0,Section on Berlekamp-Hensel & related algorithms for polynomials over finite fields,1,0,

,21,0,0,0,0,0,Berriochoa, E.,Cachafeiro, A.,,A family of Sobolev orthogonal polynomials on the unit circle,J. Comput. Appl. Math.,105,,,1999,163,173,,1,0,

,27,0,0,0,0,0,Farahmand, K.,,,Topics in Random Polynomials,,,Addison-Wesley-Longman,Harlow, U.K.,1998,0,0,Roots of Polynomials with randomly distributed coefficients,1,0,

,3,12,0,0,0,0,Herzberger, J.,,,On the R-Order of Convergence of a Class of Simultaneous Methods for the Inclusion of Polynomial Roots, in "Scientific Computing & Validated Numerics" ed. G. Alefeld,,,Akademie-Verlag,,1996,154,159,Gives interval versions of Weierstrass' & Ehrlich's methods,1,0,

,10,11,0,0,0,0,Saveleva, N.V.,,,Computer Algebra Procedures for Separating the Roots of Algebraic Equations,Comput. Math. Math. Phys.,39,,,1999,1537,1552,Uses determinants involving sums of roots & Bezout matrices,1,0,

,20,0,0,0,0,0,Tchebichef, P.L.,,,Teoria delle Congruenze,,,E. Loescher,Rome,1895,0,0,,1,0,

,10,0,0,0,0,0,Grabiner, D.J.,,,Descartes' Rule of Signs: Another Construction,Amer. Math. Monthly,106,,,1999,854,855,Gives ways of constructing polynomials having maximum number of positive and negative roots allowed by Descartes' Rule,1,0,

,19,31,0,0,0,0,Scheffler, H.,,,Beitrage zur Theorie der Gleichungen,,,Foerster,Leipzig,1891,0,0,,1,0,

,7,0,0,0,0,0,Wu X.,Wu H.,,On a class of quadratic convergence iteration formulae without derivatives,Appl. Math. Comput.,107,,,2000,77,80,Work per iteration = 2 function evaluations and 5 operations,1,0,

,19,13,0,0,0,0,Cossali, D.P.,,,Origine, trasporto in Italia, primi progressi in essa dell'Algebra. Vol II,,,,,0,0,0,Detailed treatment of cubic, quartic,1,0,

,29,0,0,0,0,0,Hayashi, T.,,,The Pancavimsatika in Its Two Recensions: A Study in the Reformation of a Medieval Sanskrit Mathematical Textbook,Indian J. History Sci.,26,,,1991,399,448,Treatment of square roots.,1,0,

,19,0,0,0,0,0,Rosen, F.,,,The algebra of Mohammed ben Musa,,,Georg Olms,Hildesheim,1986,,,Treats quadratic,1,0,

,2,17,29,0,0,0,Borwein, J.M.,Borwein, P.B.,,On the complexity of familiar functions and numbers,SIAM Rev.,30,4,,,1988,589,601,Considers square roots and evaluation of polynomials by FFT,1,0,

,13,0,0,0,0,0,Wang, Hs'iao-t'ung,,,Arithmetic in Nine Sections,,,,,650,0,0,,1,0,

,13,0,0,0,0,0,Hsia Luan-hsiang,,,Shao-kuang Chui-t'sang,,,,,1850,0,0,,1,0,

,19,0,0,0,0,0,Ting Ch'u-chung,,,Pai-fu-t'ang,,,,,1876,0,0,Deals with square roots,1,0,

,21,0,0,0,0,0,He, M.,,,Numerical results on the zeros of Faber polynomials for m-fold symmetric domains, in "Exploiting symmetry in applied and numerical analysis", ed. E.L. Allgower et al,,,American Math. Soc.,,1994,229,240,,1,0,

,25,0,0,0,0,0,Galois, E,,,Oevres V-X,,,,Paris,1897,1,61,Solutions by radicals,1,0,

,1,0,0,0,0,0,Xavier, C.,Iyengar, S.S.,,Introduction to Parallel Algorithms,,,Wiley,,1998,0,0,Describes a parallel version of the Bisection method,1,0,

,2,17,0,0,0,0,Flanders, H.,,,Scientific Pascal 2/E,,,Springer-Verlag,New York,1996,0,0,Gives Pascal programs for Newton's method and evaluation of polynomials,1,0,

,1,2,0,0,0,0,Ortega, James M,Grimshaw,,An Introduction to C++ and Numerical Methods,,,Oxford University Press,,1998,0,0,Describes Bisection, Newton and gives a C++ program combining the two.,1,0,

,19,0,0,0,0,0,Palter, R.M.,,,Towards Modern Science Vol. 1,,I,,New York,1962,0,0,Early quadratics in Egypt,1,0,

,13,0,0,0,0,0,Safiev, R.A,,,On a modification of the method of tangent hyperbolas (Russian),Dokl. Akad Nauk Azerbaidzan,19,,,1963,3,8,,1,0,

,29,0,0,0,0,0,L'Huillier, H.,,,Concerning the method employed by Nicolas Chuquet for the extraction of cube roots. In "Mathematics from Manuscript to Print 1300-1600", C.Hay (ed),,,Clarendon press,Oxford,1988,89,95,Number split into slices of 3 digits, starting from right. Find integer cube root of group on left, and subtract its cube from left-most group. And so on.,1,0,

,27,0,0,0,0,0,Renganathan, N.,Sambandham, M.,,On the lower bounds of the number of real roots of a random algebraic equation.,Indian J. Pure Appl. Math,13,,,1982,148,157,Estimates stated bound when coefficients are dependent variables with mean zero and an exponential joint density function.,1,0,

,20,0,0,0,0,0,Mines, R.,Richman, F.,,Separability and factoring polynomials,Rocky Mountain J. Math.,12,,,1982,91,102,Factoring over finite fields,1,0,

,3,12,0,0,0,0,Atanassova, L.,Herzberger, J.,,A general approach to a class of single-step methods for the simultaneous inclusion of polynomial zeros in "Validation Numerics: Theory & Appls." ed R. Albrecht et al.,,,Springer-Verlag,,1993,11,19,Uses interval methods,1,0,

,17,0,0,0,0,0,Blum, L.,Shub, M.,,Evaluating rational functions: Infinite precision is finite cost and tractable on average,SIAM J. Comput.,15,,,1986,384,398,Considers loss of precision in evaluating a rational function: the average loss is small.,1,0,

,17,29,0,0,0,0,Tienari, M.,,,On some topological properties of numerical algorithms,BIT,12,,,1972,430,433,Considers errors in arithmetic, including evaluating a polynomial, & taking a square root.,1,0,

,2,0,0,0,0,0,McMullen, C.,,,Braiding of the attractor and the failure of iterative algorithms.,Invent. Math.,91,,,1988,259,272,Gives a generally convergent algorithm for cubics, but shows such does not exist for degree>=4,1,0,

,28,0,0,0,0,0,Meir, A.,Sharma, A.,,Span of linear combinations of derivatives of polynomials.,Duke Math. J.,34,,,1967,123,130,,1,0,

,29,0,0,0,0,0,Muller, C.,,,Die Mathematik der Sulvasutra,Abh. Math. Sem. Hamburg Univ.,7,,,1930,173,204,Gives ancient Indian formula for $\sqrt{2}$ ,1,0,

,29,0,0,0,0,0,Ramanujacharia, N.,Kaye, G.R.,,The Trisatika of Sridharacarya,Bibl. Math. Ser. 3,13,,,1913,203,217,Covers ancient Indian approximation to square-roots,1,0,

,28,0,0,0,0,0,Sasaki T.,,,A theorem for separating close roots of a polynomial and its derivatives.,ACM SIGSAM Bull.,38-3,,,2004,85,92,Seperates close roots (a cluster) from the others.,1,0,

,30,0,0,0,0,0,Niu X.-M.,Sakurai T.,,A method for finding the zeros of polynomials using a companion matrix,Japan J. Ind. Appl. Math.,20,,,2003,239,256,Finds multipule roots by matrix method.,1,0,

,27,0,0,0,0,0,Samal, G.,,,Number of real zeros of a random algebraic polynomial.,Indian J. Math.,20,,,1978,225,232,If coefficients are independent random variables with expectation 0, 3rd moment finite and not 0, then number of real roots > ε_nlog n, and ε_n is a sequence tending to 0 and ε_nlog n → ∞,1,0,

,27,0,0,0,0,0,Sambandham, M.,,,On the upper bound of the number of real roots of a random algebraic equation,J. Indian Math. Soc.,42,,,1978,15,26,If coefficients are dependent with normal distribution, the equations have at most α(log log n)² log n roots.,1,0,

,29,0,0,0,0,0,Michel, P.H.,,,De Pythagore à Euclid. Contribution à l'histoire des mathématiques préeuclidiennes.,,,,Paris,1950,0,0,Treats $\sqrt{2}$ ,1,0,

,21,0,0,0,0,0,Nicolas, J.L.,Schinzel, A.,,Localisation des zeros de polynômes intervenant en théorie du signal, in"Cinquante Ans de Polynômes", Ed. M. Langevin and M. Waldschmidt,,,Springer-Verlag,New York,1990,167,179,Considers zeros of f(z) = zⁿ⁺¹-(n+1)z+n, and another similar special polynomial.,1,0,

,21,0,0,0,0,0,Nulton, J.D.,Stolarsky, K.B.,,Zeros of certain trinomials,C.R. Math. Rep. Acad. Sci. Cananda,6,,,1984,243,248,If λ fixed, between 0 and 1, and large, then P_n(z) = λzⁿ+1-λ-(λz+1-λ)ⁿ has a zero inside unit circle iff λ is not = reciprocal of a positive integer.,1,0,

,20,0,0,0,0,0,Seelhoff, P.,,,Auflösung der Congruenz x² ≡ r(mod N),Z. Math. Phys.,31,,,1886,378,380,,1,0,

,20,0,0,0,0,0,Wertheim,,,Elemente der Zahlentheorie,,,,,1887,182,183,Also see pp 207-217. Presents theory of x² ≡ a(mod m),1,0,

,19,25,0,0,0,0,Mourey, C.V.,,,La vrai théorie des quantités négatives et des quantités prétendues imaginaires,,,Mallet-Bachelier,Paris,1861,0,0,Deals with roots of cubic, and existence of a root for any equation.,1,0,

,19,0,0,0,0,0,Bertrand, J.,,,"Traité élémentaire d'Algèbre",,,Hachette,Paris,1851,0,0,Treats quadratic equations in usual manner.,1,0,

,2,10,0,0,0,0,Haase, G.,Herzberger, J.,,Schranken für die positive Wurzel von Polynomen in der Finanzmathematik,Z. Angew.Math. Mech.,78 S,,,1998,931,932,,1,0,

,15,16,0,0,0,0,Hernández, M.A.,Salanova, M.A.,,Indices of convexity and concavity. Application to Halley Method,Appl. Math. Comput.,103,,,1999,27,49,Gives conditions for convergence of Halley's method in terms of logarithmic convexity of f and f'.,1,0,

,2,7,10,19,25,0,von Burg, A.,,,Compendium der höheren Mathematik,,,Wien,,1851,0,0,Early treatment of existence, Newton's method, Sturm Sequences, low degree polynomials.,1,0,

,13,0,0,0,0,0,Vahlen,,,Über reductible Binome,Acta Math.,19,,,1895,195,198,,1,0,

,27,0,0,0,0,0,Cramer, H.,Leadbetter, M.R.,,The moments of the number of crossings of a level by a stationary normal process.,Ann. Math. Statist.,36,,,1965,1656,1663,,1,0,

,17,0,0,0,0,0,Barrio, R.,Sabadell, J.,,A Parallel Algorithm to Evaluate Chebyshev Series on a Message Passing Environment,SIAM J. Sci. Comput.,20,,,1999,964,969,A parallel algorithm to evaluate polynomials in Chebyshev form takes ∼ 4[ $\log_{2} p] +$ 4[N/p]-7 steps on p processors.,1,0,

,17,0,0,0,0,0,Reif, J.H.,,,Approximate complex polynomial evaluation in near constatnt work per point.,SIAM J. Comput.,28,,,1999,2059,2089,To evaluate at m ≥ n complex points; let Q(z_j) be an ε-approximation of P(z) and |P| = Σ|coefficients|; k = log(|P|/ε). We evaluate at m ≥ n log n/log²k points in work O(log² logn) per point.,1,0,

,17,0,0,0,0,0,Olver, F.W.J.,,,A new Approach to Error Arithmetic,SIAM J. Numer. Anal.,15,,,1978,368,393,Gives expression for error in evaluating a polynomial.,1,0,

,2,7,16,0,0,0,Argyros, I.K.,Szidarovsky, F.,,The Theory and Application of Iteration Methods,,,CRC Press,,1993,0,0,Treats Secant, Newton, Convergence.,1,0,

,29,0,0,0,0,0,Chambers, L.G.,,,An algorithm for the p'th root,Math. Gaz.,83,,,1999,258,260,Uses $x_{n + 1} = x_{n} \frac{x_{n}^{p} + λa}{λ x_{n}^{p} + a}$ where λ= $\frac{p + 1}{p - 1}$ . The method is 3rd order,1,0,

,2,15,0,0,0,0,Crandall, R.,,,Topics in Advanced Scientific Computation,,,Springer-Verlag,New York,1996,0,0,If f(a) = f''(a)=...= $f^{(m - 1)} (a) = 0 and f' (a) \neq 0,$ then $x_{n + 1} = x_{n} - \frac{f (x_{n}) f' (x_{n})}{{f' (x_{n})}^{2} - f (x_{n}) f'' (x_{n}) / m}$ has order m+1,1,0,

,2,0,0,0,0,0,Cayley, A.,,,On the Newton-Fourier Imaginary Problem,Proc. Cambridge Phil. Soc.,3,,,1880,231,232,Not able to find regions of attraction for Newton's method for cubic equation. Can for quadratic.,1,0,

,18,0,0,0,0,0,Ray, G.A.,,,A locally parameterized version of Lehmer's problem, in "Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics", ed. W. Gautschi,,,Amer. Math. Soc.,,1994,573,576,Considers whether there exist polynomials with integer coefficients such that Mahler's M(p) is close to 1. Here M(p)= | $a_{n} | Π_{i = 1}^{n}$ max{| $r_{i} |$ ,1}. Solves the problem in some cases,1,0,

,11,0,0,0,0,0,Gleyse, B.,Moflik, M.,,The Exact Computation of the Number of Zeros of a Real Polynomial in the Open unit Disk: An Algebraic Approach,Comput. Math. Appl.,39(1),,,2000,209,214,Answer in terms of Variations in sign of minors of a matrix similar to the Schur-Cohn matrix.,1,0,

,15,0,0,0,0,0,Drakopoulos, V.,,,On the additional fixed points of Schröder iteration functions associated with a one-parameter family of cubic polynomials.,Comput. And Graphics,22,,,1998,629,634,Schröder iterations applied to a cubic have fixed points which satisfy equations of order > 3. We detect points or cycles not corresponding to desired roots.,1,0,

,29,0,0,0,0,0,Datta, B.,Singh, A.N.,,Approximate Values of Surds in Hindu Mathematics,Indian J. History Sci.,28,,,1993,265,275,Gives series for $\sqrt{2}$ , correct to 5D. Also mentions the Bakhshali formula for general square root, among others.,1,0,

,21,0,0,0,0,0,Rovder, J.,,,Zeros of the polynomial solutions of the differential equation xy''+(β₀+ β₁x+ β₂x²)y'+(γ-nβ₂x)y = 0,Matematicki Casopis,24,,,1974,15,20,,1,0,

,17,0,0,0,0,0,Pan, V.Y.,Reif, J.H.,Tate, S.R.,The Power of Combining the Techniques of Algebraic and Numerical Computing: Improved Approximate Multipoint Polynomial Evaluation..in "Proc. 32nd IEEE Symp. Founds. Comp. Sci.",,,IEEE,Pittsburgh,1992,703,713,Developes a multipoint algorithm for evaluation of a polynomial of degree n at m+1 points with error bound 2^-uΣ |p_I| of order m log² u +n min{u,log n}. Parallelization is easy.,1,0,

,29,0,0,0,0,0,Hooper, A.,,,Makers of Mathematics,,,,New York,1948,0,0,Gives Pythagorean method for $\sqrt{2}$ ,1,0,

,20,0,0,0,0,0,Allenby, R.B.J.T.,Redfern, E.J.,,Introduction to number theory with computing,,,Edward Arnold,,1989,0,0,Considers congruences of high order , I.e. find integer u such that f(u) = 0 (mod m),1,0,

,2,0,0,0,0,0,Argyropoulos, N.,Böhm, A.,Drakopoulos, V.,Julia and Mandelbrot-like sets for higher order König rational iteration functions, in "Fractal Frontiers", M.M. Novak and T.G. Dewey (Eds),,,World Scientific,Singapore,1997,169,178,,1,0,

,29,0,0,0,0,0,Channabasappa, M.N.,,,On the Square-Root Formula in the Bakhshali Manuscript,Indian J. History Sci.,11,,,1976,112,124,Gives $\sqrt{Q}$ = $\sqrt{A^{2} + b}$ = A+ $\frac{b}{2 A}$ - $\frac{({\frac{b}{2 A})}^{2}}{2 (A + \frac{b}{2 A})}$ .,1,0,

,19,29,0,0,0,0,Srinivasiengar, C.N.,,,The History of Ancient Indian Mathematics,,,World Press,Calcutta,1967,0,0,Treats square & cube roots, quadratics, some cubics.,1,0,

,19,,0,0,0,0,Gupta, R.C.,,,Centenary of Bakhshali's Manuscript Discovery,Ganita Bharati,3,,,1981,103,105,The manuscript has early Indian Mathematics, e.g. quadratics,1,0,

,19,0,0,0,0,0,Shao, S.P.,Shao, L.P.,,Mathematics for Management and Finance, 6th ed.,,,South-Western Publ. Comp.,Cincinatti,1990,0,0,Covers Quadratics,1,0,

,5,25,0,0,0,0,Sturm, C.,,,D'un Théorème de M. Cauchy, relatif aux racines imaginaires des Equations,J. Math. Pures Appl.,1,,,1836,278,289,Tests whether a closed contour contains a zero of a polynomial. Proves existence of root.,1,0,

,19,0,0,0,0,0,Feldman, Richard Jr.,,,The Cardano-Tartaglia Dispute,Mathematics Teacher,54,,,1961,160,163,Historical only. (No formulas),1,0,

,190,0,0,0,0,0,Grant, E. ed.,,,A Source Book in Medieval Science,,,Harvard Univ. Press,Cambridge, Mass,1974,0,0,Gives original articles by Al-Kharizmi & others on quadratics,1,0,

,29,0,0,0,0,0,Shukla, K.S.,Sarma, K.V.,,Aryabhatiya of Aryabhata,I,,Ind. Nat. Acad. Sci.,New Delhi,1976,0,0,Gives method for square and cube roots of large integers.,1,0,

,20,0,0,0,0,0,Apostol, T.M.,,,Introduction to Analytic Number Theory,,,Springer,,1979,0,0,Considers polynomial congruences,1,0,

,17,0,0,0,0,0,von zur Gathen, J.,Strassen, V.,,Some polynomials that are hard to compute,Theoret. Comput. Sci.,11,,,1980,331,336,,1,0,

,19,0,0,0,0,0,Morley, H.,,,Jerome Cardan. The Life of Girolamo Cardano, of Milan, Physician,,,Chapman & Hall,London,1854,0,0,Reprinted Xerox University Microfilms, (1976). Treats solution of cubic historically; dispute with Tartaglia etc.,1,0,

,13,0,0,0,0,0,Delagny,,,Nouveaux Elémens d'Arithmetique et d'Algèbre,,,,Paris,1697,0,0,,1,0,

,13,0,0,0,0,0,Hume, J.,,,Algèbre de Viete, d'une méthode nouvelle, claire et facile,,,,Paris,1636,0,0,,1,0,

,13,0,0,0,0,0,Hérigone, P.,,,Cursus Mathematicus II,,,,Paris,1642,0,0,,1,0,

,13,0,0,0,0,0,Rolle, M.,,,Traité d'Algèbre ,,,,,,1690,0,0,,1,0,

,19,29,0,0,0,0,Simon, M.,,,Geschichte der Mathematik im Altertum,,,,Berlin,1909,0,0,Considers quadratics, roots,1,0,

,21,0,0,0,0,0,Gilewicz, J.,Leopold, E.,,Location of the Zeros of Polynomials satisfying three-term recurrence relations with complex coefficients,Integral Trans. & Special Functions,2,,,1994,267,278,It shows that this new method of optimization is sharp in the following sense: it leads to the exact interval where all zeros of classical orthogonal polynomials are located.,1,0,

,3,16,0,0,0,0,Milovanovic, G.V.,Petkovic, M.S.,,Computational Efficiency of the Simultaneous Methods for Finding Polynomial Zeros; Estimation of Efficiency, in "Numerical Methods & Approx. Theory, Novi Sad, 1985",,,,,1985,83,94,A Measure of efficiency of simultaneous methods for determination of polynomial zeros, defined by the so-called coefficient of effficiency, is considered in the paper.,1,0,

,16,0,0,0,0,0,Herzberger, J.,,,Wissenschaftliches Rechnen. Chap 7,,,Akademie Verlag,,1995,0,0,Considers order of convergence.,1,0,

,5,0,0,0,0,0,Kravanja, P.,Sakurai, T.,Van Barel, M.,On locating clusters of zeros of analytic functions.,BIT,39,,,1999,646,682,Finds all zeros with multiplicities contained within a Jordan curve.,1,0,

,17,0,0,0,0,0,Bauer, W.,Rabin, M.O.,,Linear Disjointness and Algebraic Complexity in "Logic and Algorithmic: an International Symposium held in Honour of E. Specker",,,Enseign. Math.,Geneva,1982,35,46,Considers preprocessing coefficients before evaluation,1,0,

,20,0,0,0,0,0,Stark, H.M.,,,An Introduction to Number Theory,,,MIT Press,Cambridge, Mass.,1979,0,0,Section on polynomial congruences.,1,0,

,17,0,0,0,0,0,Aldaz, M. et al,,,Time-Space Tradeoffs in Algebraic Complexity Theory,J. Complexity,16,,,2000,2,49, $For evaluation of polynomials of degree d we$ show Time x Space ≥ $\frac{d}{8}$ . Hence usually Space ≥.c $\sqrt[4]{d}$ ,1,0,

,1,2,0,0,0,0,Pan, V.Y.,,,Approximating Complex Polynomial Zeros: Modified Weyl's Quadtree Construction and Improved Newton's Iteration,J. Complexity,16,,,2000,213,264,Time of order n²log n log bn to get all roots with error bound 2^-bmax|z_j|,1,0,

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s2cb11,2,,,,,,Chen T.-C.,,,SCARFS; an efficient polynomial zero-finder in "Proc. Int'l Conf. on APL",,,Toronto,Canada,1993,47,54,,1,,

s2cb12,15,,,,,,Chen T.-C.,,,Convergence in iterative polynomial root-finding in "Proc. Workshop on Numerical Analysis and Applications" eds. L. Vulkov and J. Wasniewski,,,Springer-Verlag,,1997,98,105,,1,,

s2cb13,3,,,,,,Chen T.-C.,Luk W.-S.,,Aberth's method for the parallel iterative finding of polynomial zeros in "APL94 Conference Proceedings",,,Antwerp,Belgium,1994,40,49,,1,,

s2cb14,21,,,,,,Chihara T.S.,,,The three-term recurrence relation and spectral properties of orthogonal polynomials in "Orthogonal Polynomials: Theory and Practise" P. Nevai Ed.,,,Kluwer,Dordrecht,1990,99,114,,1,,

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s2cb25,19,,,,,,Colebrooke H.T. Transl.,,,"Algebra with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bhascara",,,John Murray,London,1973,,,,1,,

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s2cb30,5,,,,,,Collins G.E.,Krandick W.,,An efficient algorithm for infallible complex root isolation in "Proc. Internat. Symp. on Symbolic and Algebraic Computation" ed. P.S. Wang,,,ACM Press,Baltimore Maryland,1992,189,194,,1,,

s2cb31,2,,,,,,Collins G.E.,Krandick W.,,A Hybrid Method for High Precision Calculation of Polynomial Real Roots in "Proc. Intern. Symposium on Symbolic and Algebraic Computation",,,ACM Press,,1993,47,52,,1,,

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,29,0,0,0,0,0,Wong, W.F.,Goto, E.,,Fast Evaluation of the Elementary Functions in Single Precision,IEEE Trans. Computers,44,,,1995,453,457,Covers square root,1,0,

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,28,0,0,0,0,0,Popoviciu T.,,,Sur certaines inégalités entre les zéros, supposés tous réels, d'un polynome et ceux de sa dériveée,Ann. Sci. Univ. Jassy,30,,,1948,191,218,No note.,1,0,

,28,0,0,0,0,0,Walsh J.L.,,,A new generalization of Jensen's theorem on the zeros of the derivative of a polynomial.,Amer. Math. Monthly,68,,,1961,978,983,Zeros of derivative.,1,0,

,3,12,0,0,0,0,Sum F.,Li X.,,On an accelerating quasi-Newton circular iteration,Appl. Math. Comput.,106,,,1999,17,29,Interval simultaneous method.,1,0,

,17,0,0,0,0,0,Hasegawa T.,,,Error analysis of Clenshaw's algorithm for evaluating derivatives of a polynomial.,BIT,41-5,,,2001,1019,1028,Errors in evaluating derivatives of a polynomial expanded in orthogonal polynomials.,1,0,

,31,0,0,0,0,0,Carstensen C.,,,Linear construction of companion matrices.,Lin. Alg. Appl.,149,,,1991,191,214,Finds roots via matrices.,1,0,

,21,0,0,0,0,0,Ganelius T.,,,The zeros of the partial sums of power series.,Duke Math. J.,30,,,1963,533,540,Title says it.,1,0,

,11,0,0,0,0,0,Garloff J.,Wagner D.G.,,Hadamard products of stable polynomials are stable.,J. Math. Anal. Appl.,202,,,1996,797,809,If roots of two polynomials in left-half plane, this remains true for their product.,1,0,

,30,0,0,0,0,0,Day D.,Romero L.,,Roots of polynomials expressed in terms of orthogonal polynomials.,SIAM J. Numer. Anal.,43,,,2005,1969,1987,Roots expressed as eigenvalues of a companion matrix.,1,0,

,20,0,0,0,0,0,King J.D.,,,Integer roots of polynomials.,Math. Gaz.,90,,,2006,455,456,To find integer roots of a polynomial with integer coefficients.,1,0,

,2,0,0,0,0,0,Ujevic N.,,,An iterative method for solving nonlinear equations.,J. Comput. Appl. Math,201,,,2007,208,216,Combines Newton with a method based on integration. Sometimes converges when Newton diverges.,1,0,

,7,0,0,0,0,0,Chen J.,,,New modified regula falsi method for nonlinear equations.,Appl. Math. Comput.,184,,,2007,965,971,Stefensen-like methods combined with regula falsi give robust method with quadratic convergence.,1,0,

,15,0,0,0,0,0,Pakdemirli M.,Boyaci H.,,Generation of root-finding algorithms via perturbation theory and some formulas.,Appl. Math. Comput.,184,,,2007,783,788,Uses up to 3rd derivative. Order not stated.,1,0,

,2,0,0,0,0,0,Kou J.,Li Y.,Wang X.,A composite fourth-order iterative method for solving nonlinear equations.,Appl. Math. Comput.,184,,,2007,471,475,Order 4 with 3 evaluations. Good efficiency.,1,0,

,7,0,0,0,0,0,Wu Q.,Ren H.,Bi W.,Convergence ball and error analysis of Muller's method.,Appl. Math. Comput.,184,,,2007,464,470,Considers radius of region from which Muller's method converges.,1,0,

,15,0,0,0,0,0,Sharma J.R.,,,A family of third-order methods to solve nonlinear equations by quadratic curves approximation.,Appl. Math. Comput.,184,,,2007,210,215,Considers several methods using 2nd derivative, some more efficient than Newton.,1,0,

,15,0,0,0,0,0,Noor M.A.,Noor K.I.,,Modified iterative methods with cubic convergence for solving nonlinear equations.,Appl. Math. Comput.,184,,,2007,322,325,Third order using 2nd derivative.,1,0,

,2,0,0,0,0,0,Reese A.,,,A quasi-shrinking rectangle algorithm for complex zeros of a function.,Appl. Math. Comput.,185,,,2007,96,114,Uses a random number generator to select points in a rectangle, finds which gives lowest value of function, then shrinks the rectangle so as to still contain that point.,1,0,

,25,0,0,0,0,0,Dunham W.,,,Euler and the fundamental theorem of algebra,College Math. J.,22,,,1991,282,293,Euler gave partial proof of existence,1,0,

,25,0,0,0,0,0,Petrova S.,,,The first proof of the fundamental theorem of algebra,Fiz.-Mat. Spis B'Igar. Akad. Nauk,13,,,1970,205,210,,1,0,

,15,0,0,0,0,0,Kou J.,Li Y.,,A variant of Chebyshev's method with sixth-order convergence.,Numer. Algs.,43,,,2006,273,278,Uses 4 evaluations to get order 6.,1,0,

,25,0,0,0,0,0,Bewersdorff J.,,,Galois Theory for Beginners: A Historical Perspective.,,,Amer. Math. Soc.,,2006,0,0,Solution by radicals.,1,0,

,17,0,0,0,0,0,Petersen W.P.,Arbenz P.,,Introduction to Parallel Computing.,,,Oxford UP,,2004,0,0,Brief section on evaluation.,1,0,

,15,0,0,0,0,0,Noor M.A.,Noor K.I.,,Improved iterative methods for solving nonlinear equations.,Appl. Math. Comput.,184,,,2007,270,275,3rd order using 2nd derivative.,1,0,

,15,0,0,0,0,0,Petkovic M.S.,,,Comments on the Basto-Semiao-Calheiros root finding method.,Appl. Math. Comput.,184,,,2007,143,148,Compares the cited method with several other third-order ones. It is equal or worse.,1,0,

,15,0,0,0,0,0,Kou J.,Li Y.,Wang X.,Fourth-order iterative methods free from second derivative.,Appl. Math. Comput.,184,,,2007,880,885,Uses 3 evaluations to give 4th order.,1,0,

,3,0,0,0,0,0,Petkovic M.S.,Petkovic L.D.,,Construction of zero-finding methods by Weierstrass functions.,Appl. Math. Comput.,184,,,2007,351,359,Derives known simultaneous methods in a simple way.,1,0,

,19,0,0,0,0,0,Kalman D.,White J.,,A simple solution of the cubic,College Math. J,29,,,1998,415,418,Allegedly simple solution of the cubic- takes 3 pages.,1,0,

,19,29,10,25,0,0,Katz V.J.,,,A History of Mathematics- an Introduction,,,Harper Collins,New York,1993,0,0,Treats square roots, quadratic, cubic, existence, Descartes rule.,1,0,

,19,0,0,0,0,0,Oglesby E.J.,,,Note on the algebraic solution of the cubic,Amer. Math. Monthy,30,,,1923,321,323,Gives Cardan's solution by a different method.,1,0,

,19,0,0,0,0,0,Pen-Tung Sah, A.,,,A uniform method of solving cubics and quartics.,Amer. Math. Monthy,52,,,1945,202,206,Uses determinants.,1,0,

,19,0,0,0,0,0,Suen R.Y.,,,Roots of cubics via determinants.,College Math. J.,25,,,1994,115,117,Uses an auxillary quadratic and determinants to give "easily remembered" solution of cubic.,1,0,

,19,0,0,0,0,0,White C.R.,,,Definitive solutions of general quartic and cubic equations.,Amer. Math. Monthy,69,,,1962,285,287,No note.,1,0,

,19,0,0,0,0,0,White J.E.,,,Cubic Equations (a Mathwright workbook) on web-page www.mathwright.com/book_pgs/book241.html,The New Mathwright Library (web pg.),,,,0,0,0,Explains Cardan's solution and generalizes to higher order.,1,0,

,19,25,0,0,0,0,Calinger R. (ed),,,Classics of Mathematics,,,Moore Publishing,Oak Park Illinios,1982,0,0,Original papers on low-degree polynomials and existence.,1,0,

,21,0,0,0,0,0,van Doorn, E.A.,,,On a class of generalized orthogonal polynomials with real zeros, in "Orthogonal polynomials and their applications", ed. C Brezinski et al,,,Baltzer,Basel,1991,231,236,,1,0,

,21,0,0,0,0,,Förster, K.-J.,Petras, K.,,On the zeros of ultraspherical polynomials and Bessel functions, in "Orthogonal polynomials and their applications", ed. C Brezinski et al,,,Baltzer,Basel,1991,257,262,,1,0,

,21,0,0,0,0,0,Gori, l.,Lo Cascio, M.L.,,On an invariance property of the zeros of some s-orthogonal polynomials, in "Orthogonal polynomials and their applications", ed. C Brezinski et al,,,Baltzer,Basel,1991,277,280,,1,0,

,19,0,0,0,0,0,Vogel, K.,,,Leonardo of Pisa, in "Dictionary of Scientific Biography", Vol. 4,,,,New York,1971,604,613,Gives geometric problems leading to quadratics,1,0,

,11,0,0,0,0,0,Bose, N.K.,Shi, Y.Q.,,Network realizability approach to stability of complex polynomials,IEEE Trans. Circuits Systems,34,,,1987,216,218,,1,0,

,25,,0,0,0,0,Malfatti,,,Dubbj Proposti al Socio Paolo Ruffini Sulla Sua Dimostrazione Della Impossibilita di Risolvere le Equazioni Superiori al Quarto Grado,Mem. Mat. Fiz. Ser. Ital. Sci.,11,,,1804,579,607,Considers solution by radicals for degree > 4,1,0,

,25,0,0,0,0,0,Ruffini, P.,,,Riflessioni Intorno al Metodo Proposta dal Consocio Malfatti per la Soluzione Delle Equazioni di 5 Grado,Mem. Mat. Fiz. Soc. Ital. Sci.,12,,,1805,321,336,Considers solution by radicals for degree > 4,1,0,

,25,0,0,0,0,0,Ruffini,,,Riposta di Paolo Ruffini al Dubbj Propostigli dal Socio Gian-Francesco Malfatti Sopra la Insolubilita' Algebraica Dell' Equazioni di Grado Superiore al Quarto.,Mem. Mat. Fiz. Soc. Ital. Sci.,11,,,1804,213,267,No note.,1,0,

,2,15,19,0,0,0,Stroud K.A.,,,Further Engineering Mathematics,,,MacMillan,London,1986,0,0,Treats cubic, quartic, Newton's method, and one involving second derivative.,1,0,

,19,0,0,0,0,0,Munem M.A.,Foulis D.J.,,Algebra and Trigonometry with Applications,,,Worth Publ.,New York,1982,0,0,Treats quadratic.,1,0,

,25,0,0,0,0,0,Abel N.H.,Galois E.,,Abhandlungen über die algebraische Auflösung der Gleichungen.,,,Springer,Berlin,1889,0,0,Treats solubility by radicals.,1,0,

,2,24,0,0,0,0,Nitsche J.,,,Praktische Mathematik,,,Bibl. Inst.,Mannheim,1968,0,0,Covers Newton, and acceleration.,1,0,

,2,14,24,26,0,0,Noble B.,,,Numerical Methods 1,,,Oliver & Boyd,Edinburgh,1964,0,0,Covers Newton & Bairstow methods, acceleration and errors.,1,0,

,19,29,0,0,0,0,Gunther S.,,,Geschichte der Mathematik 1,,,,Leipzig,1908,0,0,Early treatment of surds; cubic and quartic solution.,1,0,

,19,0,0,0,0,0,Vygodsky M.,,,Mathematical Handbook: Elementary Mathematics,,,Mir Publ.,Moscow,1979,0,0,Treats quadratic.,1,0,

,3,15,0,0,0,0,Petkovic M.S.,Vranic D.V.,,The Convergance of Euler-like Method for the Simultaneous Inclusion of Polynomial Zeros.,Comput. Math. Appl.,39 (8),,,2000,95,105,Uses circular arithmetic; gives fourth order convergence & safe initial conditions.,1,0,

,2,4,7,16,17,18,Werner H.,,,Praktische Mathematik 1,,,Springer,Berlin,1970,0,0,Covers Newton, Secant, Convergence, Muller, Evaluation, Graeffe, Fourier-Budan and Bounds.,1,0,

,2,6,7,14,24,0,Morris J.L.,,,Computational Methods in Elementary Numerical Analysis,,,Wiley,New York,1983,0,0,Treats Newton, QD, Secant, Bairstow, and Acceleration.,1,0,

,19,0,0,0,0,0,Enriques F.,,,La Matematiche Nella Storia e Nella Cultura.,,,Zanichelli,Bologna,1938,0,0,Brief treatment of cubic.,1,0,

,3,12,16,0,0,0,Petkovic M.S.,Trajcovic M.,,On the R-order of convergence of dependent sequences involved in iterative processes, in "Proc. VIII Conf. Appl. Math." ed. Jacimovic,,,,,1993,197,206,Analyses R-order of convergence of dependant sequences, including interval methods.,1,0,

,2,4,0,0,0,0,McNeary S.S.,,,Introduction to Computational Methods for Students of Calculus.,,,Prentice-Hall,,1973,0,0,Elementary treatment of Newton and Graeffe's methods.,1,0,

,1,2,7,0,0,0,Pizer S.M.,Wallace V.L.,,To Compute Numerically,,,Little, Brown & Co.,Boston,1983,0,0,Treats Bisection, Newton, Secant, and Hybrid methods. Good treatment of errors.,1,0,

,0,0,0,0,0,0,Bini D.,Pan V.,,Parallel Polynomial Computations by Recursive Processes, in "ISSAC '90",,,ACM Press,New York,1990,294,0,No note.,1,0,

,19,29,0,0,0,0,Becker O.,Hoffmann J.E.,,Geschichte der Mathematik,,,Athenaum-Verlag,Bonn.,1951,0,0,Brief treatment of surds & low degree polynomials.,1,0,

,10,0,0,0,0,0,Sturm, C.,,,Sur la résolution des équations numériques,Bulletin de Férussac,12,,,1829,318,0,No note.,1,0,

,10,20,0,0,0,0,Wang P.,,,Parallel Polynomial Operations: a progress report, in "Proc. PASCO '94", ed Hong H.,,,RISC,Linz,1994,394,404,Considers parallel factorization mod primes, and GCD's.,1,0,

,10,0,0,0,0,0,Collins G.E. et al,,,Parallel Real Root Isolation Using the Coefficient Sign Variation Method, in "Computer Algebra and Parallelism" ed Zippel R.,Proc. Second Intern. Workshop,,Springer-Verlag,,1990,71,87,Uses Descartes rule of signs and bisection.,1,0,

,3,0,0,0,0,0,Iliev, A,,,A Generalization of Obreshkoff-Erlich Method for roots of Polynomial Equations,C.R.Acad Bulgare Sci.Math.Nat.,49,,,1996,23,26,Useful if multiplicities known,1,0,

,19,0,0,0,0,0,Notari, V.,,,Equzione de Quarto Grado,Perio. Mat.,4,,,1924,327,334,Historical treatment of quartic.,1,0,

,19,0,0,0,0,0,Karpinski,,,The origin and developement of algebra,School Sci. Math.,23,,,1923,54,64,Early treatment of quadratic,1,0,

,19,29,0,0,0,0,Dedron, P.,Itard, J.,,Mathématiques et mathématiciens,,,Open Univ. Press,,1973,0,0,Roots and quadratics,1,0,

,2,19,0,0,0,0,Pearson, Carl E. (ed),,,Handbook of Applied Mathematics,,,Van Nostrand Rhinehold,New York,1983,0,0,Treats low-degree and Newton,1,0,

,2,19,0,0,0,0,Stephenson, G.,,,Mathematical methods for Science Students,,,Longman,London,1973,0,0,Treats cubic and Newton's method,1,0,

s2rj19,18,,,,,,Riddell R.C.,,,Location of the zeros of a polynomial relative to a certain disk,Trans. Amer. Math. Soc.,205,,,1975,37,45,,1,,

s2rj20,13,,,,,,Risler J.-J.,Ronga F.,,Testing Polynomials,J. Symb. Comput.,10 No. 1,,,1990,1,5,,1,,

s2rj21,16,,,,,,Ritter K.,,,Average errors for zero finding: lower bounds for smooth or monotone functions,Aequationes Math.,48,,,1994,194,219,,1,,

s2rj22,16,,,,,,Ritter K.,,,Some Average Case Results for Nonlinear Numerical problems,Z. Angew. Math. Mech.,76 Supp. 3,,,1996,120,123,,1,,

s2rj23,19,,,,,,Roberts M.,,,Note sur les équations du quatrième degré,Nouv. Ann. Math.,18,,,1859,87,89,,1,,

s2rj24,21,,,,,,Ronveaux A.,Zarbo A.,Godoy E.,Fourth-order differential equations satisfied by the generalized co-recursive of all classical orthogonal polynomials. A study of their distribution of zeros.,J. Comput. Appl. Math.,59,,,1995,295,328,,1,,

s2rj25,20,,,,,,Rónyai L.,,,Factoring polynomials modulo special primes,Combinatorica,9,,,1989,199,206,,1,,

s2rj26,20,,,,,,Rónyai L.,,,Galois groups and factoring polynomials over finite fields,SIAM J. Discrete Math.,5,,,1992,345,365,,1,,

s2rj27,25,,,,,,Rosen M.I.,,,Niels Hendrik Abel and Equations of the Fifth Degree,Amer. Math. Monthly,102,,,1995,495,505,,1,,

s2rj28,31,,,,,,Rossi C.,,,Sopra la risoluzione generale per serie delle equazioni algebriche,Giorn. Mat.,44,,,1906,279,290,,1,,

s2rj29,20,,,,,,Rothschild L.P.,Weinberger P.J.,,Factoring polynomials over algebraic number fields,ACM Trans. Math. Software,2,,,1977,335,350,,1,,

s2rj30,20,,,,,,Rothstein M.,Zassenhaus H.,,Deterministic analysis of aleatoric methods of polynomial factorization over finite fields,J. Number Theory,47,,,1994,20,42,,1,,

s2rj31,18,,,,,,Rubinstein Z.,Melas A.D.,,Polynomials With No Zeros in a Disk,Amer. Math. Monthly,103,,,1996,177,181,,1,,

s2rj32,19,,,,,,Runge C.,,,über die auflösbaren Gleichungen von der form x⁵+ux+ν=0,Acta Math.,7,,,1886,173,186,,1,,

s2rj33,19,,,,,,Rutherford W.,,,New and Simple Process for Determining the Three Roots of a Cubic Equation,The Mathematician,2,,,1850,257,259,,1,,

s2rb1,2,7,15,16,,,Rabinowitz P.,,,"Numerical Methods for Nonlinear Equations",,,Gordon and Breach,London,1970,,,,1,,

s2rb2,2,19,29,,,,Rashed R.,,,"The Developement of Arabic Mathematics: Between Arithmetic and Algebra",,,Kluwer,Dordrecht,1994,,,,1,,

s2rb3,19,,,,,,Rashed R.,Ahmad S.,,"Al-bakir en Algèbre d'As-Samawal",,,University of Damascus,,1972,,,,1,,

s2rb4,19,,,,,,Rashed R.,Djebbar A. eds,,"L'Oeuvre algèbrique d'al-Khayyam",,,,Paris,1980,,,,1,,

s2rb5,28,,,,,,Rassias M. Th.,,,On certain properties of polynomials and their derivative in "Topics in Mathematical Analysis" ed. Th. M. Rassias,,,World Scientific,,1989,758,802,,1,,

s2sj62,13,,,,,,Stern,,,Remarques sur une théorème énoncé par M. Fourier,J. Reine. Angew. Math.,9,,,1832,305,311,,1,,

s2sj63,9,30,,,,,Stewart G.W.,,,On the convergence of Sebastiao e Silva's method for finding a zero of a polynomial,SIAM Rev.,12,,,1970,458,460,,1,,

s2sj64,8,,,,,,Stolan J.A.,,,An improved \v{S}iljak's algorithm for solving polynomial equations converges quadratically to multiple roots,J. Comput. Appl. Math.,64,,,1995,247,268,,1,,

s2sj65,28,,,,,,Storozhenko E.A.,,,A problem of Mahler on the zeros of a polynomial and its derivative,Mat. Sb.,187,,,1996,735,744,,1,,

,11,0,0,0,0,0,Hollot C.V.,Yang F.,,Robust stablilization of interval plants using lead or lag compensators,Syst Control Lett.,14,,,1990,9,12,Relies on result on uncertain polynomials,1,0,

,11,0,0,0,0,0,Li Y.,Nagpal K.,Lee E.B.,Stability analysis of polynomials with coefficeints in a disk,IEEE Trans. Automat. Control,37,,,1992,509,513,No note,1,0,

,11,0,0,0,0,0,Panier E.R.,Fan M.K.H.,Tits A.L.,On the robust stability of polynomials with no cross-coupling between the perturbations in the coefficients of even or odd parts.,Systems Control Lett.,12,,,1989,291,299,Stability of a subset guarantees that of a certain family,1,0,

,11,0,0,0,0,0,Pujara L.R.,,,On the stability of uncertain polynomials with dependant coefficients.,IEEE Trans. Automat. Control,AC-35,,,1990,756,759,No note.,1,0,

,11,0,0,0,0,0,Tempo R.,,,A dual result to Kharitonov's theroem.,IEEE Trans. Automat. Control,AC-35,,,1990,195,198,Stability of a family of polynomials depends on four extreme ones.,1,0,

,11,0,0,0,0,0,Tesi A.,Vicino A.,,A new fast algorithm for robust stability analysis of control systems with linearly dependant parametric uncertainites,Systems Control Lett.,13,,,1989,321,329,Considers where coefficients are affine in uncertainty parameters,1,0,

,11,0,0,0,0,0,Tesi A.,Vicino A.,,Robustness anaylsis for linear dynamical systems with linearly correlated parametric uncertainties,IEEE Trans. Automat. Control,AC-35,,,1990,186,191,No note,1,0,

,13,0,0,0,0,0,Barros M. de P.,Lind L.F.,,On the splitting of a complex-coefficient polynomial,Inst. Elec. Eng. Proc. G, Electronic Circuits Syst,133 no.2,,,1986,95,98,Splits into 2 related lower-degree polynomials,1,0,

,11,0,0,0,0,0,Siljak D.D.,,,Parameter space methods for robust control design: a guided tour,IEEE Trans. Automat. Control,AC-34,,,1989,674,688,Considers characteristic equations,1,0,

,11,0,0,0,0,0,Argoun M.B.,,,Frequency domain conditions for the stability of perturbed polynomials,IEEE Trans. Automat. Control,32,,,1987,913,916,Title says it,1,0,

,11,0,0,0,0,0,Barmish B.R.,Tempo R.,Hollot C.V. and Kang H.I.,An extreme point result for robust stability of a diamond of polynomials,IEEE Trans. Automat. Control,AC-37,,,1992,1460,1462,A family of polynomials with real coefficients in a diamond is stable iff 8 extreme polynomials are stable,1,0,

,11,0,0,0,0,0,Chapellat H.,Bhattacharyya S.P.,Dahleh M.,Robust stability of a family of disc polynomials,Internat. J. Control,51,,,1990,1353,1362,No note,1,0,

,11,0,0,0,0,0,Chen J.,Fan M.K.H.,Nett C.N.,"The structured singular value and stability of uncertain polynomials: a missing link", in: Control of Systems with Inexact Dynamic Models eds. Sadegh N. and Chen Y.H.,,,ASME,New York,1991,15,23,No note,1,0,

,13,0,0,0,0,0,Guggenbuhl L.,,,Mathematics in Ancient Egypt: A Checklist (1930-1965),Math. Teacher,58,,,1965,630,634,Contains a partial Bibliography on Egyptian math,1,0,

,19,0,0,0,0,0,King C.,,,Leonardo Fibonacci,Fibonacci Quarterly,1,,,1963,15,17,Leonardo solved a cubic,1,0,

,11,0,0,0,0,0,Barmish B.R.,,,New tools for robustness anaylsis, in "Proc. IEEE CDC",,,,,1988,1,6,Surveys applications of Kharitonov's theorem,1,0,

,20,0,0,0,0,0,Ronyai L.,Szanto A,,Prime-field-complete functions and factoring polynomials over finite fields,Comput. Artif. Intell.,15,,,1996,571,577,No note,1,0,

,20,0,0,0,0,0,Agou, S.,,,Factorisation sur un corps fini k des polynömes à coefficients composé f(x^s) lorsque f(x) est un polynöme irreductible de k[x],C. R. Acad. Sci. Paris,282,,,1976,1067,1068,Finds degrees of divisors of f(x^s),1,0,

,20,0,0,0,0,0,Mertens F.,,,Über die Irreductibilitat der Function x^p-A,Monatsch. Math. Phys.,2,,,1891,291,292,,1,0,

,20,0,0,0,0,0,Kronecker L.,,,Beweis dass für jede Primzahl p die Gleichung 1+x+x²+…+x^n-1=0 irreductibel ist,J. Reine Angew. Math.,29,,,1845,280,0,,1,0,

,11,0,0,0,0,0,Faedo S.,,,Un nuovo problema di stabilita per le equazione algebrich a coefficienti reali,Ann. Scuola Norm. Sup. Pisa. Sci. Fisc. Mat.,(Ser 3) 7,,,1953,53,63,No note,1,0,

,3,0,0,0,0,0,Iliev A.,,,A generalization of Obreshkoff-Ehrlich method for multiple roots of polynomial equations,C.R. Acad. Bulgare Sci. Sci. Math. Nat.,49,,,1996,23,26,Useful if multiplicities known,1,0,

,19,0,0,0,0,0,Notari V.,,,L'equazione di quarto grado,Period. Mat. (Ser. 4),4,,Rome,1924,327,334,Historical treatment of quartic,1,0,

,19,0,0,0,0,0,Karpinski,,,The origin and development of algebra,School Sci. Math,23,,,1923,54,64,Early treatment of quadratic,1,0,

,13,0,0,0,0,0,Pinter A.,,,Zeros of the sum of polynomials,J. Math. Anal. Appl.,270,,,2002,303,305,Gives bound for number of simple and distinct zeros of f+g, where f and g are relatively prime.,1,0,

,21,0,0,0,0,0,Davidson M.,,,On the Farey series and outer zeros of the partition polynomials,J. Math. Anal. Appl.,269,,,2002,431,443,Coeffs all 0 or 1 or -1,1,0,

,11,0,0,0,0,0,Hollot C.V.,Bartlett A.C.,,Some dicrete time counterparts to Kharitonov's stability criteria for uncertain systems,IEEE Trans. Automat. Control,31,,,1985,355,356,,1,0,

,17,0,0,0,0,0,Sedgwick R.,,,Algorithms in C++,,,Addison-Wesley,Reading, MA,1992,0,0,,1,0,

,2,0,0,0,0,0,Ritter I.F.,,,The multiplicity function of an equation (Abstract),Bull. Amer. Math. Soc.,63,,,1957,240,240,Estimate of multiplicity helps convergence of modified Newton's method.,1,0,

,1,2,7,17,10,4,Williams P.W.,,,Numerical Computation,,,Harper & Row, inc.,New York,1972,0,0,Treats Bisection, Newton, Secant, Sturm, Bairstow, QD, Lehmer-Schur, and Graeffe,1,0,

s2aj16,19,,,,,,Alexandre R.,,,Méthode et formule pour la résolution des équations du troisième degré,Nouv. Ann. Math. Ser. 2,9,,,1870,293,302,,1,,

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,10,0,0,0,0,0,Beckermann, B.,Labahn, G.,,A Fast and Numerically Stable Euclidean-Like Algorithm for Detecting Relatively Prime Numerical Polynomials,J. Symb. Comput.,26,,,1998,691,714,Considers the question of when 2 polynomials are relatively prime, even after small perturbations of the coefficients.,1,0,

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,2,0,0,0,0,0,Bachman G.,,,Introduction to p-adic Numbers and Valuation Theory,,,Academic Press,New York and London,1964,0,0,Proves conditions for convergence of Newton's method.,1,0,

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,25,,,,,,Abel N.H.,,,"Collected Works Vol. 1",,,,Christiana,1881,28,34,see also pp66-87; 478; and Vol. 2 217-244,1,,

,19,,,,,,Anon,,,Irreducible Case in " Penny Cyclopaedia Vol.13",,,Charles Knight,London,1839,38,39,,1,,

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,29,0,0,0,0,0,Cohen A.M.,,,Approximating square roots and cube roots.,Math. Gaz.,67,,,1983,221,223,Shows that a method of Grant's is equivalent to Newton's method.,1,0,

,20,0,0,0,0,0,Schwarz St.,,,On the reducibility of polynomials over a finite field.,Quart. J. Math. Oxford (Ser. 2),7,,,1956,110,124,,1,0,

,19,0,0,0,0,0,Sullivan J.W.N.,,,The History of Mathematics in Europe.,,,Oxford Univ. Press,,1925,0,0,Brief history of Cubic and Quartic,1,0,

,19,29,0,0,0,0,Lam, L.Y.,,,A Critical Study of the Yang Hui Suan Fa; A Thirteenth-Century Chinese Mathematical Treatise.,,,,,,0,0,Medieval Chinese roots and quadratics.,1,0,

,19,25,0,0,0,0,Fink K.,,,A Brief History of Mathematics. Trans. W.W. Beman and D.E. Smith.,,,Paul Kegan,London,1900,0,0,History of low degree polynomials; non-solubility by radicals of higher degree; solution by elliptic integrals.,1,0,

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,1,2,0,0,0,0,Pan V.Y.,,,New techniques for approximating complex polynomial zeros, in "5th Annual ACM-SIAM Sympos. on Discrete Algorithms",,,ACM Press,New York,1994,260,270,Uses 2-D bisection method, proximity test, and improved Newton's method.,1,0,

,10,25,0,0,0,0,Bôcher,,,Introduction to Higher Algebra,,,,,1907,0,0,Treats existence and GCD's,1,0,

,25,0,0,0,0,0,Bôcher,,,Gauss's "Third proof of the fundamental theorem of algebra",Bull. Amer. Math. Soc.,1,,,1895,205,,Relates fundamental theorem to Theory of Functions and Potential Theory,1,0,

,23,0,0,0,0,0,Baker,,,A balance for the solution of algebraic equations,Amer. Math. Monthly,11,,,1904,224,224,Describes a mechanical method,1,0,

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,29,0,0,0,0,0,Curtze, M.,,,Petri Philomeni de Dacia in Algorismum Vulgarem Johannis de Sacrobosco Commentarius,,,A.F. Host,,1897,0,0,Mediaeval Treatment of Square and Cube Roots,1,0,

,25,0,0,0,0,0,Ruffini, P.,,,Teoria Generale delle Equazioni, in cui si Dimostra Impossibile la Soluzione Algebraica delle Equazioni Generali di Grado Superiore al Quarto, in "Opere Matematiche Vol. 1", ed. E. Bortolotti,,,,,1915,0,0,,1,0,

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,19,0,0,0,0,0,Bombelli,,,L'algebra parte maggiore dell'arithmetica,,,,Bologna,1572,0,0,,1,0,

,1,2,3,12,0,0,Alefeld, G.,Herzberger, J.,,Introduction to Interval Computations. Chap. 7,,,Academic Press,New York,1983,0,0,,1,0,

,3,18,12,25,0,0,Rump, S.M.,,,Solving Algebraic Problems with High Accuracy in "A New Approach to Scientific Computation" eds. U. Kulisch, W.L. Miranker,,,Academic Press,New York,1983,51,120,Considers Interval Methods, including simultaneous,1,0,

,19,0,0,0,0,0,Ciotti, J.,,,Some Methods for Constructing the Parabola,Math. Teacher,67,,,1974,428,430,,1,0,

,19,0,0,0,0,0,Smith, Brother Albertus,,,A "Stencil Method" fpr Solving Quadratics of the Type ax² + bx + c = 0 That have Real Roots,Math. Teacher,72,,,1979,661,667,Geometric method for quadratic,1,0,

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,19,29,0,0,0,0,Ang Tian-Se,Swetz, F.J.,,A brief chronological and bibliographic guide to the History of Chinese Mathematics,Historia Math.,11,,,1984,39,56,,1,0,

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,19,0,0,0,0,0,Neugebauer O.,,,Beitrage zur Geschichte der babylonischen Arithmetik,Quellen u.Studien z. Geschichte der Math.,1,,,1930,120,130,Babylonian treatment of quadratics,1,0,

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,19,0,0,0,0,0,Ho, Peng Yoke,,,The Lost Problems of the Chang Ch'iu-chien Suan Ching, a fifth-century Chinese Mathematical Manual.,Orïens Extremus.,12,,,1965,37,37,Early Chinese quadratic solution.,1,0,

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s2xj4,2,15,,,,,Yau L.,Ben-Israel A.,,The Newton and Halley Methods for Complex Roots,Amer. Math. Monthly,105,,,1998,806,818,,1,,

s2xj5,19,25,,,,,Young G.P.,,,Principles of the Solution of Equations of the Higher Degrees; with Applications,Amer. J. Math.,6,,,1884,65,102,,1,,

s2xj6,19,25,,,,,Young G.P.,,,Resolution of Solvable Equations of the Fifth Degree,Amer. J. Math.,6,,,1884,103,114,,1,,

s2xj7,19,25,,,,,Young G.P.,,,Solution of Solvable Irreducible Quintic Equations; without the aid of a Resolvent Sextic,Amer. J. Math.,7,,,1885,170,177,,1,,

s2xj8,19,25,,,,,Young G.P.,,,Solvable Irreducible Equations of Prime Degree,Amer. J. Math.,7,,,1885,271,278,,1,,

s2xj9,18,,,,,,Young J.R.,,,New Criteria for the Imaginary Roots of Equations,Phil. Mag.,22,,,1843,186,188,see also ibid 23 (1843) 450-452,1,,

s2xj10,25,,,,,,Young J.R.,,,Remarks on the problem of the general solution of algebraic equations,Mechanics' Magazine,48,,,1848,101,102,,1,,

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s2xj13,20,,,,,,Zassenhaus H.,,,über die Fundamentalkonstruktionen der endlichen Körpertheorie,Jahres. Deutscher Math.-Verein.,70,,,1968,177,181,,1,,

s2xj14,19,,,,,,Zeuthen H.G.,,,Sur l'origine de l'Algebre,Danske Vid. Selsk. Mat.-Fys. Medd.,No. 4,,,1919,,,,1,,

s2xj15,3,14,,,,,Zheng S.M.,,,Linear interpolation and parallel iteration for splitting factors of polynomials,J. Computational Mathematics (Beijing),4,,,1986,146,153,,1,,

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,19,0,0,0,0,0,Rodet L.,,,Leçons de Calcul d'Aryabhata,Journal Asiatique (Ser. 7),13,,,1879,393,434,Brief mention of quadratic,1,0,

,19,0,0,0,0,0,Busard H.L.L.,,,L'algèbre au Moyen Age: le "liber mensurationum" d'Abu Bekr,Journal des savants,,,,1968,65,124,Arabic treatment of quadratic,1,0,

,19,0,0,0,0,0,Karpinsky L.C.,,,Robert of Chester's latin translation of the algebra of Al-Khowarizmi, in "Contributions to the History of Science",,,Univ. Michigan,Ann Arbor,1930,0,0,Arabic treatment of quadratic,1,0,

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,19,0,0,0,0,0,McLaurin C.,,,A second letter to Martin Foulkes concerning the Roots of Aequations with the Demonstration of other Rules in Algebra,Philos. Trans. Roy. Soc. London,36,,,1729,59,96,Gives method of telling if roots are real,1,0,

,20,0,0,0,0,0,Kaltofen E.,Shoup V.,,Subquadratic-Time factoring of Polynomials over Finite Fields, in "Proc. 27th ACM Symp. Theory of Computing",,,,,1995,398,406,Time O(n^1.815),1,0,

,10,0,0,0,0,0,Yun D.Y.Y.,,,Uniform bounds for a class of algebraic mappings,SIAM J. Comput.,8,,,1979,348,356,Deals with GCD's,1,0,

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,20,0,0,0,0,0,Niven, I.,Zuckerman, H.,,An Introduction to the Theory of Numbers,,,J. Wiley,New York,1960,0,0,Treats quadratic congruences;existence of roots,1,0,

,20,0,0,0,0,0,Adams, W.,Goldstein, L.,,Introduction to Number Theory,,,Prentice-Hall,New Jersey,1976,0,0,Treats polynomial congruences,1,0,

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,20,0,0,0,0,0,Leveque, W.J.,,,Topics in Number Theory,,,Addison-Wesley,Reading, Mass.,1958,0,0,Considers polynomial congruences briefly.,1,0,

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,19,0,0,0,0,0,Chuquet, N.,,,La Géométrie,,,,Paris,1979,0,0,Geometric treatment of square and cube roots,1,0,

,21,0,0,0,0,0,Lagomasino, G.L.,Cabrera, H.P.,Izquierdo, I.P.,Sobolev Orthogonal polynomials in the complex plane,J. Comp. Appl. Math,127,,,2001,219,230,Treats zeros of certain special polynomials,1,0,

,30,32,0,0,0,0,Ammar, G.S. et al,,,Polynomial Zerofinders based on Szegö polynomials,J. Comp. Appl. Math,127,,,2001,1,16,Applies eigenvalue and continuation methods to equivalent Szego polynomials,1,0,

,19,29,0,0,0,0,King, D.A.,Saliba, G.,,From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kenedy,,,New York Acad. Of Science,New York,1987,0,0,Has articles on quadratics and roots.,1,0,

,21,0,0,0,0,0,Jackson, Bill,,,A Zero-free Interval for Chromatic Polynomials of Graphs,Combinatorics, Prob. And Comput.,2,,,1993,325,336,Shows that P(G,t) has no zeros in [1,32/27]. It is known it has none in (-∞,1),1,0,

,21,3,30,0,0,0,Pasquini, L.,,,On the computation of the zeros of the Bessel polynomials, in "Approximation and Computation", ed R.V.M. Zaher,,,Birkhauser-Verlag,Boston,1994,511,534,Compares simultaneous root-finding with eigenvalue methods, for solutions of 2nd order differential equations.,1,0,

,17,0,0,0,0,0,Sedgewick, R.,,,Algorithms,,,Addison-Wesley,Reading, Mass.,1989,0,0,Considers evaluation,1,0,

,13,29,0,0,0,0,Lam, L.Y.,,,Chu Shih-chieh's "Introduction to mathematical studies",Arch. Hist. Exact Sci.,21,,,1979,1,31,Brief treatment of high order nth roots and equations.,1,0,

,13,29,0,0,0,0,Lam, L.Y.,,,The Chinese connection between the Pascal triangle and the solution of numerical equations of any degree.,Historia Math.,7,,,1980,407,424,Brief treatment of high order nth roots and equations,1,0,

,13,19,0,0,0,0,Libbrecht, U.,,,Chinese mathematics in the thirteenth century, the Shu-shu chiu-chang of Ch'in Chiu-shao,,,MIT Press,Cambridge, Mass.,1973,0,0,Treats a variation of Homer's method,1,0,

,25,0,0,0,0,0,Dickson,,,On the theory of equations in a modular field,Bull. Amer. Math. Soc.,13,,,1906,8,,Deals with Galois resolvents,1,0,

,19,0,0,0,0,0,Tropfke, J.,,,Zur Geschichte d. quadratischen Gleichungen uber dreienhalb Jahrtausende,Jahresber. Deutsch. Math.-Verein,43,,,1933,98,107,Early treatment of quadratic,1,0,

,29,0,0,0,0,0,Saidan, A.,,,The Arithmetic of Al-Uqlidisi,,,D. Reidel,Dordrecht,1978,0,0,Early Arabic treatment of square roots etc.,1,0,

,29,0,0,0,0,0,Tannery, P.,,,L'extraction des racines carrées d'après Nicolas Chuquet,Bibl. Math. Ser. 2,1,,,1887,17,21,Mediaeval treatment of square roots,1,0,

,13,0,0,0,0,0,Blanchard, P.,,,Complex analytic dynamics on the Riemann sphere,Bull. Amer. Math. Soc. (New. Ser.),11,,,1984,85,141,Considers orbits of polynomials,1,0,

,29,0,0,0,0,0,Bryuno, A.D.,,,Continued fraction expansion of algebraic numbers,USSR Comput. Math. and Math. Phys.,4,,,1964,1,15,

Gives expansions of $\frac{1}{\sqrt[3]{2}} etc .$

,1,0,

,29,0,0,0,0,0,Lang, S.,Trotter, H.,,Continued fractions for some algebraic numbers,J. Reine Angew. Math.,255,,,1972,112,134,

Gives continued fractions for some surds such as $\sqrt[3]{2}$ etc.

See p 219-220 also,1,0,

,29,0,0,0,0,0,von Neuman, J.,Tuckerman, B,,Continued fraction expansion of

$\sqrt[3]{2}$

,Math. Tab. Aids Comput.,9,,,1955,23,24,,1,0,

,29,0,0,0,0,0,Richtmyer, R.D.,Devaney, M.,Metropolis, N.,Continued fraction expansions of algebraic numbers,Numer. Math,4,,,1962,68,84,Gives Frequency Distribution of Partial Denominators for Expansion of some surds,1,0,

,13,0,0,0,0,0,Stark, H.M.,,,An explanation of some exotic continued fractions found by Brillhart, in "Computers in Number Theory", eds. A.O.L. Atkin and Birch,,,Academic Press,London,1971,21,35,,1,0,

,13,0,0,0,0,0,Roth, K.F.,,,Rational approximations to algebraic numbers,Mathematika,2,,,1955,1,20,

Shows that, for algebraic numbers α, if |α- $\frac{h}{q} | < \frac{1}{q^{k}} has infinitely many solutions \frac{h}{q}$ , then k=2.

,1,0,

,29,0,0,0,0,0,Rodet, L.,,,Sur une méthode d'approximation des racines carrés, conne dans l'Inde antérieurment à la conquête d'Alexandre,Bull. Soc. Math. France,7,,,1879,98,102,Ancient treatment of square roots,1,0,

,29,0,0,0,0,0,Rodet, L.,,,Sur les méthodes d'approximation chez les anciens,Bull. Soc. Math. France,7,,,1879,159,167,Ancient treatment of square roots,1,0,

,19,0,0,0,0,0,Woepcke, M.,,,Sur un essai de determiner la nature de la racine d'une équation du troisième degré,J. Math. Pure Appl.,19,,,1854,401,406,Refers to Leonardo of Pisa,1,0,

,10,0,0,0,0,0,Adams, W.W.,,,An Introduction to Gröbner Bases,AMS Grad St. in Mathematics,3,,,1991,0,0,Considers greatest common divisors,1,0,

,10,0,0,0,0,0,Apostol, T.M.,,,Resultants of cyclotomic polynomials,Proc. Amer. Math. Soc,24,,,1970,457,463,,1,0,

,19,0,0,0,0,0,Bortollotti, E.,,,La storia della matematica nell'università de Bologna,,,Zanichelli,Bologna,1944,0,0,History of cubic and quadratic,1,0,

,19,0,0,0,0,0,Marie, M.,,,Histoire des sciences mathématiques en Italie Vol. 3,,,Gauthier-Villars,Paris,1841,0,0,Treats cubics,1,0,

,2,7,26,0,0,0,Wang, X.H.,,,On the error estimates for some numerical root-finding methods,Acta Math. Sinica,22,,,1979,638,642,Combined Newton-Secant method; Convergence.,1,0,

,1,2,3,7,12,15,Herzberger, J.,,,Einführung in das wissen-schaftliche Rechnen,,,Addison-Wesley,Bonn,1997,0,0,A good treatment of Bisection, Newton, Secant, Muller, Intervals, Existence. Laguerre, Simultaneous methods,1,0,

,7,0,0,0,0,0,Vogel, K.,,,Die Practica des Algorismus Ratisbonensis,,,,Munich,1954,0,0,Treats Reguli Falsi,1,0,

,29,0,0,0,0,0,Ibn Labban, K.,,,Principles of Hindu Reckoning, transl. M. Levey and M. Petruck,,,Univ. of Wisconson Press,Madison, WI,1965,0,0,Early Arabic treatment of square and cube roots.,1,0,

,11,0,0,0,0,0,Gantmacher, Fr.,,,Theory of Matrices. Vol. 2,,,,Paris,1966,0,0,Treats Routh-Hurwitz criteria etc.,1,0,

,10,0,0,0,0,0,Hermite, C.,,,Remarques sur le théorème de Sturm,C.R. Acad. Sci. Paris,36,,,1853,294,297,,1,0,

,29,0,0,0,0,0,Kern, H. ed,Brill, E.J., ed,,The Aryabhatiya with the commentary Bhatadipika of Paramadicvara (Sanskrit-Text),,,, Neudruck,1972,0,0,,1,0,

,29,0,0,0,0,0,Rangacarya, M., ed.,,,Ganitasarasamgraha,,,,Madras,1912,0,0,,1,0,

,7,0,0,0,0,0,Lefebure De Fourcy, L.E.,,,Leçons d'Algèbre,,,Gauthier-Villars,Paris,1870,0,0,Newton, Secant, Sturm, low-order, square roots, Existence,1,0,

,19,0,0,0,0,0,Karpinski, L.C.,,,The Algebra of Abu Kamil,Bibl. Math. (Ser. 3),12,,,1912,40,55,Early Arabic treatment of quadratic,1,0,

,29,0,0,0,0,0,Drenckhahn, F.,,,Zur Zirkulation des Quadrats und Quadratur des Kreises in den Sulva-Sütras.,Jahres. Deutsch. Math.-Verein,46,,,1936,1,13,Treats early Indian calculation of $\sqrt{2}$ .,1,0,

,19,0,0,0,0,0,Vogel, K.,,,Die Mathematik der Babylonier,,,Vorgr. Mathematik,Hanover, Paderborn,1959,0,0,Babylonians gave formula for quadratic roots.,1,0,

,19,0,0,0,0,0,Rashed, R.,,,Récommencements de l'Algèbre au XI et XII Siècles, in "The Cultural Context of Medieval Learning", ed. J.E. Murdoch,,,Reidel,Dordrecht,1975,33,60,Describes early Arabic treatment of quadratic.,1,0,

,19,0,0,0,0,0,Sesiano, J.,,,Les Méthodes d'analyse indéterminée chez Abu Kamil,Centaurus,21,,,1977,89,105,Describes early Arabic treatment of quadratic.,1,0,

,28,0,0,0,0,0,Anderson B.,,,Polynomial Root Dragging,Amer. Math Monthly,100,,,1993,864,866,Shows how roots of derivative move as real roots of polynomials move.,1,0,

,28,0,0,0,0,0,Gelca R.,,,A Short Proof of a Result on Polynomials,Amer. Math Monthly,100,,,1993,936,937,If f has distinct real roots, so does f'-kf for real k.,1,0,

,28,0,0,0,0,0,Walker P.,,,Separation of the Zeros of Polynomials,Amer. Math Monthly,100,,,1993,272,273,Minimum distance of roots of f'-kf > that of f,1,0,

,18,0,0,0,0,0,Sylvester J.J.,,,On An Elementary proof and generalization of Sir Isaac Newton's hitherto undemonstrated rule for the discovery of imaginary roots,Proc. London Math. Soc.,1,,,1865,1,16,Gives conditions for number of positive (negative) roots,1,0,

,29,0,0,0,0,0,Schönborn,,,Uber die Methode, nach der die alten Griechen (insbesondere Archimedes und Heron),Zeit. Math. Phys,28,,,1883,169,178,Treats square roots among ancient Greeks,1,0,

,19,29,0,0,0,0,Möller,,,Die Mathematik der Sulvasutra,Abh, Math Sem Hamburg Univ.,7,,,1930,173,204,Treats roots of 2 and quadratics in early India,1,0,

,21,0,0,0,0,0,Dimitrov D.K.,,,On a conjecture concerning monotonicity of zeros of ultraspherical polynomials,J. Approx. Theory,85,,,1996,88,97,,1,0,

,21,0,0,0,0,0,Ronveaux A.,Muldoon M.,,Stieltjes sums for zeros of orthogonal polynomials,J. Comput. Appl. Math,57,,,1995,261,269,Considers sums involving zeros of derivatives also.,1,0,

,19,0,0,0,0,0,Khayyam O.,,,A paper of Omar Khayyam transl. A.R. Amir-Moex,Scripta Math.,26,,,1961,323,331,Derives and treats low-degree polynomials,1,0,

,19,0,0,0,0,0,Abu-Kamil,,,Algebra. Tr. & ed M. Levey,,,Univ of Wisconson Press,,1966,0,0,Early treatment of quadratic,1,0,

,19,0,0,0,0,0,de Nemore, J.,,,De Numeris Datis: Transl and ed B.B. Hughes,,,Univ of California Press,,1981,127,132,Treats quadratic,1,0,

,17,0,0,0,0,0,Pan V.Y.,,,Compexity of Computations with Matrices and Polynomials,SIAM Rev.,34,,,1992,225,262,Considers complexity of evaluating polynomials at one or more points.,1,0,

,6,0,0,0,0,0,Pan V.Y.,Reif, J.,,Some Polynomial and Toeplitz Matrix Computations, in "Proc. 28th IEEE Symp Found. Comp. Science",,,,,1987,173,184,Uses Turan's proximity test, Graeffe's method, Winding numbers,1,0,

,2,7,14,0,0,0,Lapidus L.,,,Digital Computation for Chemical Engineers,,,McGraw-Hill,New York,1962,0,0,Good treatment of Newton, Secant, and Bairstow methods,1,0,

,19,0,0,0,0,0,Carra de Vaux B.,,,Penseurs de l'Islam Vol. 2,,,,Paris,1921,0,0,Arabic treatment of a few quadratics,1,0,

,20,0,0,0,0,0,Rademacher H.,,,Lectures on elementary number theory,,,Blaisdell,Waltham, Mass.,1964,0,0,Deals with congruences and cyclotonic polynomials,1,0,

,2,14,26,0,0,0,Fox A.H.,,,Fundamentals of Numerical Analysis,,,The Ronald Press Co.,New York,1963,0,0,Very elementary treatment of Newton, Lin's method and convergence,1,0,

,2,7,0,0,0,0,Harris L.D.,,,Numerical Methods Using Fortran,,,Charles E Merill Bks,Columbus, OH,1964,0,0,Treats secant, inverse quadratic interpolation, and Newton,1,0,

,20,0,0,0,0,0,Davenport H.,,,The Higher Arithmetic,,,Hutchinson & Co. Publish,London,1952,0,0,Deals with congruences,1,0,

,20,0,0,0,0,0,Griffin H.,,,Elementary Theory of Numbers,,,McGraw-Hill,New York,1954,0,0,Treats congruences,1,0,

,20,0,0,0,0,0,Jones B.W.,,,The Theory of Numbers,,,Rinehart & Co.,New York,1955,0,0,Deals with Congruences,1,0,

,20,0,0,0,0,0,Stewart B.M.,,,Theory of Numbers,,,MacMillan Co.,New York,1952,0,0,Deals with Congruences,1,0,

,13,0,0,0,0,0,Maclaurin C.,,,The Collected Letters S. Mills ed.,,,Shiva Publishing Ltd,Chesire,1982,0,0,Many letters re polys of degree up to 5th.,1,0,

,10,0,0,0,0,0,Grabiner J.V.,,,Budan de Boislaurent, in Dictionary of Scientific Biography Vol. 2,,,Scribner's,New York,1970,573,574,Tells how many roots between 0 and p>0,1,0,

,25,0,0,0,0,0,Houzel C.,,,La résolution algébrique des équations, in "Sciences á l'époque de la révolution Francaise",,,Blanchard,Paris,1988,17,37,Considers resolution of 5th degree equation and related matters,1,0,

,25,0,0,0,0,0,Humbert P.,,,Les Mathématiques aux XIX Siècle, in "Histoire de la Science", M. Daumas ed.,,,Gallimard,Paris,1957,619,688,,1,0,

,10,0,0,0,0,0,Moigno F.N.W.,,,Note sur la determination du nombre des racine reeles ou imaginaires d'une equation numerique comprises entre des limites donnees,J. Math. Pure Appl.,5,,,1840,75,94,,1,0,

,19,29,0,0,0,0,Midonick H.,,,The Treasury of Mathematics,,,,London,1965,0,0,Quotes early work on surds and quadratics,1,0,

,19,0,0,0,0,0,Archibald R.C.,,,Mathematics before the Greeks,Science (N.S.),71,,,1930,109,121,Babylonian solution of quadratic,1,0,

,19,13,0,0,0,0,Hamburg, R.R.,,,The Theory of Equations in the 18th century:The Work of Joseph Lagrange,Arch. Hist. Exact Sci.,16,,,1976,17,36,Treats quadratic, cubic and uses continured fractions for higher degree in a variation of Horner's method.,1,0,

,25,0,0,0,0,0,Hungerford, T.W.A,,,A Counterexample in Galois Theory,Amer. Math. Monthly,97,,,1990,54,57,,1,0,

,20,0,0,0,0,0,Williams K.S.,,,Polynomials with irreducible factors of specified degree,Canad. Math. Bull,12,,,1969,221,223,,1,0,

,10,20,0,0,0,0,Davenport J.M. et al,,,Computer Algebra: Systems and Algorithms for Algebraic Computation,,,Academic Press,London,1988,0,0,Good treatment of sturm,gcd and polynomials with integral coefficients,1,0,

,18,0,0,0,0,0,Mignotte,,,Some useful bounds, in "Computer Algebra, Symbolic and Algebraic Computation" , Buchberger et al (eds),,,Springer,New York,1982,259,263,Gives bounds on absolute value of roots, and minimal distance between roots,1,0,

,25,19,0,0,0,0,Baumgart, J.E.,,,History of algebra,Hist. Topics for the Math. Classroom,31,,Washington,1969,233,332,Very brief history of low degree equations and existence.,1,0,

,25,0,0,0,0,0,Abel, N.H.,,,Demonstration de l'impossibilite de la resolution algebrique des equations generales qui passent le quatrieme degre, in "Oeuvres completes",Oeuvres completes,1,,,1881,66,94,Proves impossibility of solution by radicals for general equation of degree >4.,1,0,

,25,0,0,0,0,0,Euler, L.,,,Innumerae aequationum formae ex omnibus ordinibus, quarum resolutio exhiberi potest, in "Opera Omnia",Opera Omnia,6,,,0,434,446,Gives many equations of degree > 4 which can be solved by radicals.,1,0,

,25,0,0,0,0,0,Gaal L.,,,Classical Galois Theory with Examples,,,Chelsea,New York,1973,0,0,,1,0,

,21,0,0,0,0,0,Gautschi W.,Kuiijlaars A.B.J.,,Zeros and critical points of Sobolev Orthogonal Polynomials,J. Approx Theory,91,,,1997,117,137,,1,0,

,21,0,0,0,0,0,Lagomasino L.G.,Cabrera H.P.,,Zero location and nth root asymptotics of Sobolev orthogonal polynomials,J. Approx. Theory,99,,,1999,30,43,,1,0,

,21,0,0,0,0,0,Stahl H.,Totik V.,,General Orthogonal Polynomials,,,Cambridge Univ. Press,Cambridge,1992,0,0,Treats zeros of orthogonal polynomials,1,0,

,20,0,0,0,0,0,Glesser Ph,Mignotte M.,,An inequality about irreducible factors of integer polynomials(II),Proceedings of AAECC-8,,,Tokyo,1990,260,266,,1,0,

,10,20,25,0,0,0,Winkler F.,,,Polynomial Algorithmns in Computer Algebra,,,Springer-Verlag,Wien,1996,0,0,Treats GCD,factorization over finite fields and integers,1,0,

,19,0,0,0,0,0,Bortolotti E.,,,L'Algebra nella storia et nella preistoria delle Scienze,Osiris,1,,,1936,184,230,Early treatment of quadratic,1,0,

,13,0,0,0,0,0,Baron M.E.,,,William George Horner,Dict. Sci. Biog.,6,,,1972,510,511,Describes Horner's method,1,0,

,21,0,0,0,0,0,Tutte W.T.,,,Chromials, Hypergraph Seminar, ed C. Berge & D. Ray-Chaudhuri (LNM 411),,,Springer-Verlag,,1974,243,266,Brief mention of zeros,1,0,

,29,0,0,0,0,0,Brent R.P.,,,Fast multi-precision evaluation of elementary functions,J. Assoc. Comput. Mach.,23,,,1976,242,251,Shows that $\sqrt{c}$ can be evaluated, to precision n, in O(M/n) operations. Likewise root of f(x) = 0.,1,0,

,2,13,0,0,0,0,Douady A.,Hubbard J.,,Iteration des polynomes quadratiques complexes,C.R.Acad. Sci. Paris,294,,,1982,123,126,,1,0,

,5,0,0,0,0,0,Ioakimidis N.I.,Anastasselou E.G.,,A modification of the Delves-Lyness method for locating the zeros of analytic functions,J. Comput. Phys.,59,,,1985,490,492,Formula for integrals involved, not using derivatives of function,1,0,

,24,29,0,0,0,0,Cohen A.M.,,,Improving the convergence of alternating series,Internat. J. Comput. Math,9,,,1981,45,53,Applies Aitken acceleration to root finding including $\sqrt{2}$ ,1,0,

,29,0,0,0,0,0,Grant M.A.,,,Approximating square roots and cube roots,Math. Gaz.,66,,,1982,230,230,Gives approximations to square roots of 2,3,5,7,1,0,

,20,0,0,0,0,0,Ljunggren W.,,,On the irreducibility of certain trinomials and quadrinomials,Math Scand,8,,,1960,65,70,Considers irreducibility over the rationals of polynomials of the form xⁿ±x^m±x^p±1,1,0,

,20,0,0,0,0,0,Tverberg H.,,,On the irreducibility of xⁿ±x^m±1,Math. Scand,8,,,1960,121,126,Considers irreducibility over the rationals of polynomials of the stated form,1,0,

,20,0,0,0,0,0,Boyd D.W.,Montgomery H.L.,,Cyclotomic Partitions, in "Number Theory, Banff, AB." Ed R.A. Mullin,,,de Gruyter,Berlin,1990,7,25,Estimates the number of cyclotomic polynomials of degree n and how many have distinct factors,1,0,

,13,19,0,0,0,0,Tweedie C.,,,A Study of the Life and Writings of Colin MacLaurin,Math. Gaz.,8,,,1915,133,151,,1,0,

,19,0,0,0,0,0,MacLaurin C.,,,A Letter from Mr. Colin MacLaurin, Prof of Math at Edin. Etc. concerning equations with impossible roots,Phil. Trans. Roy. Soc. London,34,,,1726,104,112,Gives conditions for roots of low order equations (and general one) to be real,1,0,

,13,0,0,0,0,0,Mills S.,,,The Collected Letters of Colin MacLaurin,,,,Nantwich, Chesire,1982,0,0,,1,0,

,10,0,0,0,0,0,Benis-Sinaceur H.,,,Deux moments dans l'histoire du théorème d'Algèbre de C.F. Sturm,Rev. d'Hist. Sci.,41,,,1988,99,132,Considers original theorem of Sturm and application to logic by Tarski,1,0,

,10,0,0,0,0,0,Darboux G.,,,Note relative au mémoire (de Fourier de 1820), in "Oeuvres de Fourier" Vol. II,,,,,1890,310,314,Refers to Budan's theorem about number of roots in [0,p],1,0,

,10,0,0,0,0,0,Nicholson P.,,,New demonstration of the method invented by Budan and improved by others of extracting the roots of equations,Phil. Mag.,60,,,1822,173,178,Variation on Descartes rule,1,0,

,29,0,0,0,0,0,Chuquet N.,,,Nicholas Chiquet Renaissance Mathematician, Trans. H.G. Flegg et al,,,Reidel,,1985,144,153,Treats roots (surds),1,0,

,0,0,0,0,0,0,Brodie K.W.,,,On Bairstow's method for the solution of polynomial equations,Math. Comp.,29,,,1975,816,826,Bairstow's method is one member of a family. Other members may be better.,1,0,

,6,0,0,0,0,0,Henrici P.,,,Finding zeros of a polynomial by the Q-D algorithm,Comm. Ass. Comp. Mach.,8,,,1965,570,574,Tests on the (slowly convergent) Q-D algorithm, some failures due to equal roots,1,0,

,7,0,0,0,0,0,Miranker W.L.,,,Parallel methods for approximating the root of a function,IBM J Res Dev,13,,,1969,297,301,Uses high order interpolation,1,0,

,7,0,0,0,0,0,Miranker W.L.,,,A survey of parallelism in numerical analysis,SIAM Rev,13,,,1971,524,547,Uses high order interpolation,1,0,

,21,0,0,0,0,0,Varga R.S.,Carpenter A.J.,,Zeros of the partial sums of cos(z) and sin(z). I,Numer. Alg.,25,,,2000,363,375,Considers rates of convergence to associated Szego curves,1,0,

,21,0,0,0,0,0,Driver K.A.,Love A.D.,,Products of hypergeometric functions and the zeros of ₄F₃ polynomials,Numer. Alg.,26,,,2001,1,9,,1,0,

,6,0,0,0,0,0,Kravanja P.,Van Barel M.,,Computing the Zeros of Analytic Functions,,,Springer-Verlag,Berlin,2000,0,0,,1,0,

,13,0,0,0,0,0,Pan V.Y.,,,A New Proximity Test for Polynomial Zeros,Comput. Math. Appl.,41,,,2001,1559,1560,Computes minimum and maximum distance from a fixed point to zeroes.,1,0,

,7,0,0,0,0,0,Wu X.Y.,Xia J.L.,Shao R.,Quadratically convergent multiple roots finding method without derivatives,Comput. Math. Appl,42,,,2001,115,119,Uses formulas involving F(x_n+F(x_n)) where F(x) involves f(x+|f(x)|^1/m) and multiplicity m is assumed known,1,0,

,2,15,0,0,0,0,Gutierrez J.M.,Hernandez M.A.,,An acceleration of Newton's method: Super-Halley method,Appl. Math. Comput.,117,,,2001,223,239,Gives a new third-order method,1,0,

,20,0,0,0,0,0,Stein G.,,,Using the theory of cyclotomy to factor cyclotomic polynomials over finite fields,Math. Comp.,70,,,2001,1237,1251,Takes time about r⁵ for r'th cyclotomic polynomial,1,0,

,15,0,0,0,0,0,Kalantari B.,Park S.,,A computational comparison of the first nine members of a determinantal family of root-finding methods.,J. Comput. Appl. Math.,130,,,2001,197,204,For lower (higher) degree, lower (higher) methods best. Overall most efficient is B₄⁽⁴⁾. Newton is least efficient,1,0,

,3,11,0,0,0,0,Seen F.,Kosmol P.,,A new simultaneous method of fourth order for finding complex zeros in circular interval arithmetic,J. Comput. Appl. Math.,130,,,2001,293,307,No comparison with other methods.,1,0,

,21,0,0,0,0,0,Driver K.A.,Love A.D.,,Zeros of ₃F₂ hypergeometric polynomials,J. Comput. Appl. Math.,131,,,2001,243,251,Gives tables of zeros.,1,0,

,13,0,0,0,0,0,Ho P.Y.,,,Yang Hui,Dict. Sci. Biog.,14,,,1976,538,546,Horner's method described,1,0,

,29,0,0,0,0,0,Cody W.J.,Waite W.,,Software manual for the elementary functions,,,Prentice-Hall,Englewood Cliffs N.J,1980,0,0,Gives flow-chart for SQRT program,1,0,

,19,0,0,0,0,0,Hull T.E.,,,The use of controlled precision, in "Proc of IFIP TC2 Working Conference on the Relationship between Numerical Computation and Programming Languages",,,North Holland,Amsterdam,1982,71,84,Gives procedure for solving quadratic,1,0,

,20,0,0,0,0,0,Dimitrov D.K.,,,Connection Coefficients and Zeros of orthogonal polynomials,J. Comput. Appl. Math.,133,,,2001,331,340,,1,0,

,20,0,0,0,0,0,Elbert A.,Laforgia A.,Siafarikas P.,A conjecture on the zeros of ultraspherical polynomials,J. Comput. Appl. Math.,133,,,2001,684,0,,1,0,

,20,0,0,0,0,0,Martinez-Finkelstein A.,,,On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters,J. Comput. Appl. Math.,133,,,2001,477,488,,1,0,

,20,0,0,0,0,0,Grünbaum F.A.,,,Electrostatic interpretation for the zeros of certain polynomials and the Darboux process,J. Comput. Appl. Math.,133,,,2001,397,412,,1,0,

,11,0,0,0,0,0,Liapounoff M.A.,,,Problème générale de la stabilité du mouvement,,,Princeton Univ. Press,,1947,0,0,Considers stability (negative real part of roots).,1,0,

,7,13,0,0,0,0,Swetz F.J.,,,The amazing Chiu Chang Suan Shu,Math. Teacher,65,,,1972,423,430,Mentions Homer and Reguli Falsi in ancient China,1,0,

,13,0,0,0,0,0,Swetz F.J.,,,The evolution of mathematics in ancient China,Math. Magazine,52,,,1979,10,19,Brief mention of Horner's method in early China,1,0,

,29,0,0,0,0,0,Günther S.,,,Die quadratischen Irrationalitaten der Alten und deren Entwickelungsmethoden,Abh. Gesch. Math.,4,,,1882,1,134,Ancient treatment of square roots,1,0,

,19,0,0,0,0,0,Cantor M.,,,I sei cartelli de matematica disfida,Bull. Bibl. Storia Sci. Mat. Fis.,11,,,1878,177,196,Detailed history of cubic,1,0,

,19,0,0,0,0,0,Karpinski,,,The Algebra of Abu Kamil Shoja'ben Aslam,Bibl. Math. Ser. 3,12,,,1912,40,55,Early Arabic treatment of quadratics,1,0,

,19,0,0,0,0,0,Tropfke J.,,,Zur Geschichte d. quadratischen Gleichungen uber dreieinhalb Jahrtausende,Jahresber. Deutsch. Math-Verein.,43,,,1934,98,107,Early treatment of quadratic (see also vol 44 pp 26-47, 95-119),1,0,

,11,0,0,0,0,0,Jury, E.I.,,,On the roots of a real polynomial inside the unit circle and a stability criterion for linear discrete systems.,2nd IFAC congress,,,Basel,1963,142,153,Conditions for roots to be inside the unit circle are given in terms of 2nd order determinants.,1,0,

,11,0,0,0,0,0,Tschauner, J.,,,On the stability of sampled-data systems.,Automat. Remote Control,24,,,1963,831,836,,1,0,

,11,0,0,0,0,0,Desages, A.C..,,,Distance of a Complex Coefficient Stable Polynomial from the Boundary of the Stability Set,Multidim. Systems and Signal Process.,2,,,1991,189,210,The distance from a complex coefficient polynomial to the border of its Hurwitz region is analysed.,1,0,

,11,0,0,0,0,0,Bose, N.K.,Shi, Y.Q.,,A simple general proof of Kharitonov's generalized stability criterion.,IEEE Trans. Circuits and Systems,34,,,1987,1233,1237,Hurwitz property of a set of interval poly's depends on 8 extreme polys.,1,0,

,11,0,0,0,0,0,Petersen, I.R.,,,A class of stability regions for which Kharitonov like theorem holds.,IEEE Trans. Automat. Control.,34,,,1989,1111,1115,Determines if all polynomials in a family have all their roots in a given region.,1,0,

,11,0,0,0,0,0,Bose, N.K.,Kim, K.D.,,Stability of a complex polynomial set with coefficients in a diamond and generalization.,IEEE Trans Circuits and Systems,36,,,1989,1168,1174,Hurwitz property of complex polynomials with coefficients having real & imaginary parts within a diamond depends on 16 edges of the diamonds,1,0,

,11,0,0,0,0,0,Hinrichsen, D.,Pritchard, A.J.,,An application of state space methods to obtain explicit formulae for robustness measure of polynomials, in "Robustness In Identification and Control", ed M. Milanese,,,Plenum,New York,1989,183,206,Studies stability of polynomials under perturbations of the coefficients.,1,0,

,11,0,0,0,0,0,Chapellat, H.,Bhattacharyya, S.P.,Dahleh, M.,On the robust stability of a family of disk polynomials, in "Proc. 29th IEEE Conf. Decision & Control",,,,Tampa,1989,37,42,A set of polynomials with coefficients in disks is Hurwitz stale if the "centre" polynomial is stable, and the norms of a certain two rational functions are < 1.,1,0,

,21,0,0,0,0,0,Varga, R.S.,Carpenter, A.J.,,Zeros of the partial sums of cos(z) and sin(z),Numer. Math,90,,,2001,371,400,Title says it.,1,0,

,29,0,0,0,0,0,Taylor, J.,,,Lilavati,,,,Bombay,1816,0,0,Treats square and cube roots among Hindus,1,0,

,19,29,0,0,0,0,Jouschkewitsch, A.P.,,,Geschichte der Mathematik im Mittelalter,,,,Basel,1964,0,0,Treats roots, low degree world-wide in middle ages.,1,0,

,19,0,0,0,0,0,Franci, R.,Rigatelli, L.T.,,Gianfranco Malfatti e la teoria delle equazioni algebriche, in "Atti del Convegno 'Gianfrancisco Malfatti nella cultura del suo tempo'",,,,Ferraro,1982,179,203,Treats low degree cases.,1,0,

,19,29,0,0,0,0,Juschkewitsch, A.P.,Rosenfeld, B.A.,,Der Mathematik der Lander des Ost. In Mittelalter,,,,Berlin,1963,0,0,Covers square roots, quadratics, and up to quartics.,1,0,

,2,10,0,0,0,0,Tsai, Y.F.,Farouki, R.T.,,Algorithm 812:BPOLY: An object-oriented library of numerical algorithms in Bernstein form,ACM Trans. Math. Softw.,27,,,2001,267,296,Uses Sturm sequences and Newton's method to find real roots of polynomials in Bernstein form. These are more stable than power form, especially for high degree.,1,0,

,21,0,0,0,0,0,Mehta, M.L.,,,Properties of the zeros of a polynomial satisfying a second order linear partial differential equation,Lett. Nuov.Cim.,26,,,1979,361,362,,1,0,

,11,0,0,0,0,0,Kharitonov,,,On the generalization of a stability criterion,Izvest. Akad Nauk Kazakh. SSR. Ser Fiz-Mat,1,,,1978,53,57,,1,0,

,20,0,0,0,0,0,Sun Qui,Han Wenbao,,On absolute trace and primitive roots in finite fields,Chinese J. Contemp. Math (New York),11,,,1990,202,205,,1,0,

,19,0,0,0,0,0,Kropp, G.,,,Vorlesungen uber Geschichte der Mathematik.,,,Biblio. Inst.,Mannheim-Zurich,1969,0,0,History of cubic and quartic.,1,0,

,29,0,0,0,0,0,Boll, M.,,,Histoire des mathematiques.,,,Press. Univ. de France,,1968,0,0,Gives continued fraction for sqrt(2).,1,0,

,25,0,0,0,0,0,Malfatti, G.,,,Dubbj proposti al socio Paolo Ruffini sulla sua dimostrazione della impossibilita di risolvere le equazioni superiori al quarto grado.,Mem Mat. Fis Soc. Ital. Sci.,11,,,1804,579,607,Considers solution by radicals for degree > 4,1,0,

,19,0,0,0,0,0,de Moivre, A.,,,Aequationum quarundam Potestatis tertiae, quintae, septimae, nonae, et superiorum, ad infinitum usque pergendo, in terminis finitis, ad instar Regularum pro Cubicus, quae vocantur Cardani, resolutio analytica.,Phil. Trans. Roy. Soc. London,25,,,1707,2368,0,Describes Cardan's solution of cubic,1,0,

,3,5,0,0,0,0,Ioakimidis, N.I.,Anastesselou, E.G.,,On the simultaneous determination of zeros of analytic or sectionally analytic funtions,Computing,36,,,1986,239,247,Uses integrals to convert to polynomial problem; then uses several simultaneous methods.,1,0,

,5,30,0,0,0,0,Kravanja, P.,Van Barel, M.,Ragos, O. et al.,ZEAL: A mathematical software package for computing zeros of analytic functions,Comput. Phys. Commun.,124,,,2000,212,232,Uses integrals and eigenvalue problems,1,0,

,5,0,0,0,0,0,Kravanja, P.,Cools, R.,Haegermans, A.,Computing zeros of analytic mappings: A logarithmic residue approach.,BIT,38,,,1998,583,596,Uses integrals of logs,1,0,

,2,12,0,0,0,0,Hansen, E.,,,Global optimization using Interval Analysis,,,Marcel Dekker,New York,1992,0,0,Treats Interval Newton method and slope interval Newton method,1,0,

,3,12,0,0,0,0,Petkovic, M.,Herceg, D.,,Methods with corrections for the simultaneous inclusion of polynomial zeros,Nonlinear Analysis,30,,,1997,73,82,Uses interval methods to give bounds on zeros ( obtained simultaneously ).,1,0,

,21,0,0,0,0,0,Buendia, E.,Dehesa, J.S.,Galvez, F.J.,The distribution of zeros of the polynomial eigenfunctions of ordinary differential equations of arbitrary order, in "Orthogonal Plynomials and their Applications", M. Alfaro et al Eds,,,Springer-Verlag,Berlin,1986,222,235,,1,0,

,21,0,0,0,0,0,Zarzo, A.,Dehesa, J.S.,Ronveaux, A.,Newton sum rules of zeros of semi-classical orthogonal polynomials.,J. Comput. Appl. Math.,33,,,1990,85,96,,1,0,

,3,0,0,0,0,0,Bini, D.A.,,,Numerical computation of polynomial zeros by means of Aberth's method.,Numerical Algorithms,13,,,1996,179,200,A very robust and efficient implementation of Aberth's method, never failed on 1000 polynomials of degree up to 25,000. Uses Rouché's theorem for initial guesses.,1,0,

,19,0,0,0,0,0,Dold-Samplonius, Y.,,,The solution of quadratic equations according to al-Samaw'al, in "Mathemata, Festschrift fur Helmuth Gericke",,,Franz Steiner,Stuttgart,1985,95,104,Quadratics among Arabs.,1,0,

,13,29,0,0,0,0,Wang Ling,Needham,,Horner's method in Chinese mathematics: its origins in the root-extraction procedures of the Han dynasty.,T'oung Pao,43,,,1955,345,0,,1,0,

,5,0,0,0,0,0,Anastasselou, E.G.,Ioakimidis, N.I.,,A new approach to the derivation of exact analytical formulae for the zeros of sectionally analytic functions.,J. Math. Anal. Appl.,112,,,1985,104,109,Finds zeros of a related polynomial having integrals for coefficients,1,0,

,3,12,16,0,0,0,Atanassova, L.,,,On the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane.,J. Comput. Appl. Math.,50,,,1994,99,107,Uses high-order derivatives and fractional powers of F.,1,0,

,19,0,0,0,0,0,Kennedy, E.S.,,,Studies in the Islamic exact sciences,,,Amer. Univ. Beirut,Beirut,1983,0,0,Quadratics among Arabs,1,0,

,5,12,0,0,0,0,Herlocker, J.,Ely, J.,,An automatic and guaranteed determination of the number of roots of an analytic function interior to a simple closed curve in the complex plane,Reliable Computing,1,,,1995,239,250,Uses interval arithmetic to give bound on integral for number of roots within a curve.,1,0,

,5,0,0,0,0,0,Ioakimidis, N.I.,,,A unified Riemann-Hilbert approach to the analytical determination of zeros of sectionally analytic functions,J. Math. Anal. Appl.,129,,,1988,134,141,Uses integral formulae,1,0,

,17,0,0,0,0,0,Belaga, E.G.,,,On Computing Polynomials in One Variable with Initial Conditioning of the Coefficients,Prob. of Cyber.,5,,,1964,7,15,Describes methods of evaluation more efficient than Horner's; applies to complex numbers.,1,0,

,20,0,0,0,0,0,Dickson, L.E.,,,Introduction to the theory of numbers,,,Univ. of Chicago Press,Chicago,1957,0,0,Treats congruences.,1,0,

,15,0,0,0,0,0,Hernandez. M.A.,Salanova, M.A.,,A Family of Newton type Iterative Processes,Int. J. of Comput. Math.,51,,,1994,205,214,Studies methods such as Halley's involving higher derivatives.,1,0,

,13,0,0,0,0,0,Mellin, H.J.,,,Ein Allgemeiner Satz Über Algebraische Gleichungen,Annales Acad. Scient. Fennicae,7, No.8,,,1915,1,44,Expresses roots in terms of hypergeometric or gamma functions.,1,0,

,21,0,0,0,0,0,Dette, H.,Studden, W.J.,,Some new asymptotic properties of Jacobi, Laguerre, and Hermite polynomials,Constr. Approx.,11,,,1995,227,238,,1,0,

,10,0,0,0,0,0,Sylvester, J.J.,,,On the expressions for the quotients which appear in the application of Sturm's method to the discovery of the real roots of an equation, in "Collected Works",,,,Cambridge,1904,396,398,,1,0,

,10,18,0,0,0,0,Sylvester, J.J.,,,Note on a remarkable modification of Sturm's theorem, and on a new rule for finding superior and inferior limits to the roots of an equation,Phil. Mag.,6,,,0,14,20,Uses continued fractions,1,0,

,10,18,0,0,0,0,Sylvester, J.J.,,,On the new rule for finding superior and inferior limits to the real roots of any algebraic equation.,Phil. Mag.,6,,,0,138,140,Uses continued fractions,1,0,

,10,18,0,0,0,0,Sylvester, J.J.,,,Note on the new rules of limits,Phil. Mag.,6,,,0,210,213,Uses continued fractions,1,0,

,10,0,0,0,0,0,Sylvester, J.J.,,,On the relation of Sturm's auxillary functions to the roots of an algebraic equation, in "Collected Works",,,,Cambridge,1904,59,60,,1,0,

,13,0,0,0,0,0,Ioakimidis, N.I.,,,A note on the closed-form determination of zeros and poles of generalized analytic functions,Stud. Appl. Math.,81,,,1989,265,269,,1,0,

,21,0,0,0,0,0,Faldey, J.,Gawronski, W.,,On the limit distributions of the zeros of Jonquiere polynomials and generalized classical orthogonal polynomials,J. Approx. Theory,81,,,1995,231,249,,1,0,

,21,0,0,0,0,0,Gawronski, W.,,,Strong asymptotics and the asymptotic zero distributions of Laguerre polynomials L_n^(an+α) and Hermite polynomials H_n^(an+α),Analysis,13,,,1993,29,67,Considers limit as n-> ∞,1,0,

,26,0,0,0,0,0,Börsch-Supan, W.,,,Residuenabschätzung Polynom-Nullstellen mittels Lagrange-Interpolation,Numer. Math.,14,,,1970,287,297,Given approximations to zeros, errors are estimated. Applies to multiple roots using high derivatives of p.,1,0,

,21,0,0,0,0,0,van Assche W.,Teugels J.L.,,Second order asymptotic behaviour of zeros of orthogonal polynomials.,Rev. Roumaine Math. Pures Appl.,32,,,1987,15,26,No note.,1,0,

,21,0,0,0,0,0,Elbert A.,Laforgia A.,,New properties of the zeros of a Jacobi polynomial in relation to their centroid.,SIAM J. Math. Anal.,18,,,1987,1563,1572,No note.,1,0,

,2,0,0,0,0,0,Watson W.A.,Philipson T.,Oates P.J.,Numerical Analysis- The Mathematics of Computing.,,,Edward Arnold,London,1969,0,0,Treats Newton.,1,0,

,11,0,0,0,0,0,Katbab A.,Jury E.,,"On the generalization and comparison of two frequency-domain stability robustness results", in Proceedings of the American Cont. Conf.,,,,,1991,1969,1972,Considers stability of perturbed polynomials.,1,0,

,26,0,0,0,0,0,Elsner, L.,,,A remark on simultaneous inclusions of the zeros of a polynomial by Gershgorin's theorem,Numer. Math.,21,,,1973,425,427,Finds a postieriori bounds on errors for zeros.,1,0,

,15,0,0,0,0,0,Kalantari, B.,,,Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas and its applications.,J. Comput. Appl. Math.,126,,,2000,287,318,Uses rational functions involving x and derivatives of f.,1,0,

,29,0,0,0,0,0,Kalantari, B.,Kalantari, I.,,High order iterative methods for approximating square roots.,BIT,36,,,1996,395,399,Generalizes Newton and Halley's methods; uses higher derivatives.,1,0,

,15,0,0,0,0,0,Kalantari, B.,Kalantari, I.,Zaare-Nahandi, R.,A basic family of iteration functions for polynomial root finding and its characterizations,J. Comput. Appl. Math.,80,,,1997,209,226,Uses j'th derivative of p(x) in generalization of Newton's method.,1,0,

,21,0,0,0,0,0,Ismail, M.E.H.,,,An electrostatic model for zeros of general orthogonal polynomials,Pacific J. Math.,193,,,2000,355,369,,1,0,

,20,0,0,0,0,0,Selmer, E.S.,,,On the irreducibility of certain trinomials,Math. Scand.,4,,,1956,287,302,Shows that xⁿ -x-1 is irreducible for all n; xⁿ +x+1 for n ≠ 2 (mod 3) .,1,0,

,21,0,0,0,0,0,Grünbaum, F.A.,,,Variations on a theme of Heine and Stieltjes; An electrostatic interpretation of the zeros of certain polynomials.,J. Comput. Appl. Math.,99,,,1998,189,194,Title says it.,1,0,

,21,0,0,0,0,0,Cheng, S.S.,Lin, Y.Z.,,Detection of positive roots of a polynomial with five parameters,J. Comput. Appl. Math.,137,,,2001,19,48,Special polynomial arising in population dynamics.,1,0,

,20,0,0,0,0,0,Carmichael, R.D.,,,The Theory of Numbers & Diophantine Analyses,,,Dover,New York,1959,0,0,Treats congruences.,1,0,

,4,0,0,0,0,0,Malajovich, G.,Zubelli, J.P.,,On the Geometry of Graeffe Iteration,J. Complexity,17,,,2001,541,573,Describes a stabilized version of Graeffe's method which is almost always globally convergent. Can solve up to degree 1000.,1,0,

,25,0,0,0,0,0,Stubhaug, A.,,,Niels Henrik Abel and His Times…,,,Springer-Verlag,,2000,0,0,Historical treatment for layman.,1,0,

,25,0,0,0,0,0,Von Sohsten de Medeiros,A,,,The fundamental theorem of Algebra Revisited,Amer. Math. Monthly,108,,,2001,759,760,Proof based on Lefschetz Fixed - point theorem,1,0,

,13,19,0,0,0,0,Holm, J.,,,Les Systemes d'équations polynômes dans le Sujuan Juyian (1303),Inst. Hautes Etud. Chinoises,,,,0,0,0,Treats quadratics and higher degree in medieval China,1,0,

,19,29,0,0,0,0,Datta, B.,,,The Science of the Sulba,,,Univ . Calcutta,,1932,0,0,Treats quadratics, surds,1,0,

,10,0,0,0,0,0,Mulders, T.,Storjohann, A.,,The modulo N extended GCD problem for polynomials, in ISSAC '98, ed K.Y. Chwa,,,Springer,,1999,105,112,,1,0,

,10,0,0,0,0,0,Chin, P.,Corless, R.M.,Corliss, G.F.,Optimization strategies for the approximate GCD problem, in ISSAC '98, ed K.Y. Chwa,,,Springer,,1999,228,235,Solves an optimization problem to find coefficients of 'best' GCD when coefficients of the 2 polynomials are known inexactly,1,0,

,13,0,0,0,0,0,Hetz, M.A.,Kaltofen, E.,,Efficient algorithms for computing the nearest polynomial with constrained roots, in ISSAC'98 ed K.Y. Chwa,,,Springer,,1999,236,243,Considers finding minimal perturbation to the coefficients needed to move a root to a point or line etc.,1,0,

,3,0,0,0,0,0,Kirrinnis, P.,,,Fast numerical improvement of factors of polynomials and of partial fractions, in ISSAC'98 ed K.Y. Chwa,,,Springer,,1999,260,267,Uses multidimensional Newton method (Weierstrass),1,0,

,3,0,0,0,0,0,Petkovic, M.S.,Herzeg, D.,,Point estimation of simultaneous methods for solving polynomial equations: a survey,J. Comput. Appl. Math.,136,,,2001,283,307,Conditions for convergence of Durand-Kerner and similar methods depend only on coefficients, degree, and initial approximations to zeros.,1,0,

,12,19,0,0,0,0,Ferreira, J.A.,Patricio, F.,Oliveira, F.,A priori estimates for the zeros of interval polynomials,J. Comput. Appl. Math.,136,,,2001,271,281,Polynomials of degree 2,3,4 with interval coefficients are considered.,1,0,

,21,0,0,0,0,0,Driver, K.,Duren, P.,,Zeros of ultraspherical polynomials and the Hilbert-Klein formulas,J. Comput. Appl. Math.,135,,,2001,293,302,,1,0,

,4,0,0,0,0,0,Rice, T.A.,Siegel, L.J.,,A parallel algorithm for finding the roots of a polynomial, in "Proc 1982 Int. Conf. on Parallel Proc." Ed Batcher,K.E,,,IEEE Comp. Sci. Press,,1982,57,61,Parallel Graeffe's method,1,0,

,19,0,0,0,0,0,Weinberg, J.,,,Die Algebra des Abu Kamil Soga ben Aslam,,,,,1935,0,0,Quadratics among Arabs,1,0,

,13,0,0,0,0,0,Ruffini, P.,,,Sobra la determinazione delle radici nelle equazioni numeriche di qualunque grado, in "Opere Mat. II",,,Cremonese,,1953,281,404,,1,0,

,19,0,0,0,0,0,Giesing, J.,,,Leben und Schriften Leonardos da Pisa,,,Druck von J.W. Thallwitz,Dobeln,1886,0,0,,1,0,

,29,0,0,0,0,0,Thibaut, G.,,,On the Sulvasutras,J. of the Royal Asiatic Soc. Of Bengal,44, part 1,,,1875,252,275,,1,0,

,19,0,0,0,0,0,Lindberg, D.C. (ed),,,Science in the Middle Ages,,,Univ. of Chicago Press,Chicago,1978,0,0,Historical treatment of quadratic,1,0,

,11,0,0,0,0,0,Chen, J.,Fan, M.K.H.,Nett, C.N.,Structured singular values and stability analysis of uncertain polynomials, part 1,Syst. Control Lett.,23,,,1994,53,65,Stability with variable coefficients.,1,0,

,11,0,0,0,0,0,Chen, J.,Fan, M.K.H.,Nett, C.N.,Structured singular values and stability analysis of uncertain polynomials, part 2,Syst. Control Lett.,23,,,1994,97,109,Stability with variable coefficients.,1,0,

,11,0,0,0,0,0,Joya, K.,Furuta, K.,,Criteria for Schur and D-stability of a family of polynomials constrained with P-norm, in "Proc. IEEE Conf. Dec.and Control",,,,,1991,433,434,Stability of polynomials with constrained coefficients.,1,0,

,11,0,0,0,0,0,Kogan, J.,,,How near is a stable polynomial to an unstable polynomial?,IEEE Trans. Circuits and Systems I,39,,,1992,676,680,Given a stable polynomial, finds how much coefficients can be perturbed and still give stability.,1,0,

,11,0,0,0,0,0,Perez, F.,Abdallah, C.,Docampo, D.,Robustness analysis of polynomials with linearly correlated uncertain coefficients in l^P-normed balls, in "Proc. IEEE Conf. Dec. and Control",,,,,1994,2996,2997,Considers stability of families of polynomials .,1,0,

,11,0,0,0,0,0,Qiu, L.,Davison, E.J.,,A simple procedure for the exact stability robustness computation of polynomials with affine coefficient perturbations,Syst.Control Lett.,13,,,1989,413,420,Title says it.,1,0,

,20,0,0,0,0,0,Kraitchik. M.,,,Théorie des nombres, Vol 1,,,Gauthier-Villars et Cie.,Paris,1922,0,0,Treats congruences,1,0,

,20,0,0,0,0,0,Kraitchik. M.,,,Théorie des nombres, Vol II,,,Gauthier-Villars et Cie.,Paris,1926,0,0,Treats congruences.,1,0,

,19,0,0,0,0,0,Boyer, C.,,,A History of Mathematics,,,John Wiley & Sons,New York,1968,0,0,Treats history of quadratic and cubic in detail.,1,0,

,19,0,0,0,0,0,Carruccio, E.,,,Mathematics and Logic in History and in Contemporary Thought,,,Faber & Faber,London,1964,0,0,Discusses cubics,1,0,

,19,0,0,0,0,0,Neugebauer, O.,,,Zur Geschichte der babylonischen Mathematik,Quell. Stud. Gesch. Math.,B1,,,1929,78,80,Treats quadratics in Egypt and Babylon,1,0,

,19,0,0,0,0,0,Churchhouse,Muir,,Continued fractions, algebraic numbers, and modular invariants,J. Inst. Math. Appl.,5,,,1969,318,328,Considers continued fraction expansion of root of a cubic,1,0,

,20,0,0,0,0,0,Sierpinski, W.,,,Elementary Theory of Numbers,,,P.W.N.,Warsaw,1964,0,0,Treats congruences,1,0,

,20,0,0,0,0,0,Weil, A.,,,Number Theory for Beginners,,,Springer,,1979,0,0,Treats congruences,1,0,

,13,19,25,0,0,0,Smith, D.E.,,,A Source Book in Mathematics,,,McGraw-Hill,New York,1929,0,0,Articles by Cardan, etc on cubic, biquadratic; Abel on quintic; Galois on groups and equations; and Gauss on existence,1,0,

,20,0,0,0,0,0,Wright, H.N.,,,First Course in the Theory of Numbers,,,Wiley,New York,1964,0,0,Considers congruences,1,0,

,10,0,0,0,0,0,Bocher, M.,,,The published and unpublished work of Ch. Sturm on algebraic and differential equations,Bull. Amer. Math. Soc.,18,,,1911,1,18,Historical treatment of Sturm's theorem.,1,0,

,25,0,0,0,0,0,Dieudonné, J.,,,Abrégé d'histoire des mathématiques,,,Hermann,Paris,1978,0,0,Treats existence and solution by radicals,1,0,

,10,20,2,18,0,0,Weisner, L.,,,Theory of Equations,,,Macmillan,New York,1938,0,0,Considers Newton's method, Sturm and related theorems, bounds, rational roots.,1,0,

,19,0,0,0,0,0,Bulmer-Thomas, I.,,,Greek Mathematical Works, 2 vols,,,Harvard Univ. Press,Cambridge, Mass.,1939,0,0,Early Greek treatment of quadratic and cubic.,1,0,

,19,0,0,0,0,0,Jayawardene, S.S.,,,The Trattato d'Albaco of Piero della Francesca, in "Cultural Aspects of the Italian Renaissance…", ed Clough C.H.,,,C. Clough,Manchester,1976,229,243,Treats low-degree equations.,1,0,

,17,0,0,0,0,0,Kiper, A.,,,Parallel Polynomial Evaluation by Decoupling Algorithm,Parallel Algs. Appl.,9,,,1996,145,152,Horner's algorithm of evaluating a polynomial is studied and formulated as a matrix equation Ax=c, with a special bidiagonal A.,1,0,

,21,0,0,0,0,0,Ismail, M.E.H.,Letessier, J.,,Monotonicity of zeros of ultraspherical polynomials, in "Orthgonal Polynomials and Their Applications", Ed. M. Alfaro et al LNM 1329,,,Springer-Verlag,Berlin,1988,329,330,,1,0,

,11,0,0,0,0,0,Soh C.,,,"Frequency domain criteria for robust root location of generalized disc polynomials" in Robustness of Dyns. Sys. with Parameter Uncertainties (M. Mansour, S. Balemi, and W. Truol, eds.),,,Birkhauser,Basel,1992,23,42,Considers stability of perturbed polynomials.,1,0,

,1,2,7,16,0,0,Cheney W.,Kincaid D.,,Numerical Mathematics and Computing (2nd ed.),,,Brooks/Cole Publishing,Monterey, Calif.,1985,0,0,Treats Bisection, Newton, Secant and convergence.,1,0,

,2,7,14,0,0,0,Daniels R.W.,,,An Introduction to Numerical Methods and Optimization Techniques.,,,North-Holland,New York,1978,0,0,Treats Newton, Muller, and Bairstow.,1,0,

,2,14,0,0,0,0,Tompkins C.B.,Wilson, W.L.,,Elementary Numerical Analysis,,,Prentice-Hall, Inc.,New Jersey,1969,0,0,Treats Newton, and Bairstow,1,0,

,2,10,14,17,29,0,Locher, F.,,,Einführung in die Numerische Mathematik,,,,Darmstadt,1978,0,0,Good treatment of Newton, Sturm, Bairstow, Evaluation, and surds,1,0,

,20,0,0,0,0,0,Nagell, T.,,,Sur la recuctibilité des trinomes, in "Attonde Skand. Mat.-Kongr.",,,,,1934,0,0,,1,0,

,13,19,0,0,0,0,Anbouba, A.,,,L'Algèbre al-Badi d'Al-Karaji,,,,Beyrouth,1964,0,0,Treats quadratic and high-order polynomials,1,0,

,25,0,0,0,0,0,Ruffini, P.,,,Sur l'insolubilité des équations algébriques …, in "Oeuvres mathematiques de P. Ruffini", Vol. 2,,,,Bologna,1806,107,154,Impossibility of solving polynomials of degree > 4 by radicals,1,0,

,29,0,0,0,0,0,Luckey, P.,,,Die Ausziehung der n.-ten Wurzel und der binomische Lehrsatz in der islamischen Mathematik,Math. Ann.,120,,,1948,217,274,Treats n'th roots by Ruffini-Horner method,1,0,

,21,0,0,0,0,0,Gawronski, W.,Shawyer, B.,,Strong asymptotics and the limit distribution of the zeros of P_n^{(an+α,bn+β)}, in "Progress in Approximation Theory", ed P. Nevai,,,Academic Press,,1991,379,404,,1,0,

,25,0,0,0,0,0,Kolmogoroff, A.N.,Youschkevitch, A.P.,,Les mathématiques au 19^o siècle: Logique Mathématique, Algèbre, Théorie des Nombres, Théorie des Probabilités,,,Nauka,Moscow,1992,0,0,Covers Existence and Solution by Radicals,1,0,

,11,0,0,0,0,0,Fujiwara, M.,,,Über die Algebraischen Gleichungen, deren Wurzeln in einem kreise oder in einer Halbebene liegen,Math. Zeit.,24,,,1926,161,0,Deals with Routh-Hurwitz problem etc.,1,0,

,19,0,0,0,0,0,Toomer, G.I.,,,"Al-Khwärizmi", in Dictionary of Scientific Biography, Vol. 7,,,,,1980,358,365,Arabic solution of quadratic,1,0,

,19,0,0,0,0,0,Al-Tusi (Sharaf Al-Din),,,Oeuvres mathématiques. Algèbre et géométrie au XIIe siècle, ed. R. Rashed,,,,Paris,1986,0,0,Arabic quadratics and cubics,1,0,

,29,0,0,0,0,0,Waterhouse, W.,,,Note on a method of extracting roots in al-Samaw'al,Arch. Hist. Exact Sci.,19,,,1978,383,384,Describes a complicated method for surds which often does not work.,1,0,

,25,0,0,0,0,0,Betti, E.,,,Sulla risoluzione delle equazioni algebriche, in "Opere Mathematiche" Vol 1,,,,,0,31,80,Briefly considers conditions for solubility.,1,0,

,19,0,0,0,0,0,al-Khayyami, Umar,,,The Algebra, transl.D.S. Kasir ( The Algebra of Omar Khayyam),,,,New York,1931,0,0,Treats quadratic and early cubics.,1,0,

,19,0,0,0,0,0,al-Khayyami, Umar,,,The Algebra of Umar Khayyam, transl. H.J.J. Winter, W. Arafat,J. Royal Asiatic Soc. Bengal, Science,16,,,1950,27,70,Treats quadratic and early cubics.,1,0,

,19,0,0,0,0,0,al-Khwarizmi, M.ben Musa,,,The Algebra of Muhammed ben Musa transl. F. Rosen,,,,London,1831,0,0,Arabic quadratics,1,0,

,19,25,0,0,0,0,Tietze H.,,,Famous problems of mathematics Translation of 2nd German ed (1959),,,Graylock Press,Baltimore, Md.,1965,0,0,Actually gives solutions for cubic and quartic and brief treatment of Galois theory.,1,0,

,2,8,0,0,0,0,Voyevodin, V.V.,,,The use of the method of descent in the determination of all the roots of an algebraic polynomial,USSR Comp. Math. Math. Phys.,1 no 2,,,1961,187,195,Uses combination of Newton and method of descent,1,0,

,15,0,0,0,0,0,Hernandez, M.A.,,,An acceleration procedure of Whittaker method by means of convexity,Zbornik Radova fak. Serija matematiku,21,,,1991,27,38,Accelerates Whittaker method ie x_n=1 = x_n-λf(x_n),1,0,

,10,0,0,0,0,0,Sturm, C.,,,a l'occasion de l'article précéedent,J. Math. Pures Appl.,7,,,1842,132,133,,1,0,

,10,0,0,0,0,0,Sturm, C.,,,Demonstration d'un Théorème d'algèbre de M. Sylvester,J. Math. Pures Appl.,7,,,1842,356,368,,1,0,

,16,26,0,0,0,0,Wilkinson, J.H.,,,Practical problems arising in the solution of polynomial equations.,J. Inst. Math. Appl.,8,,,1971,16,35,Considers termination criteria, and error bounds.,1,0,

,11,0,0,0,0,0,Bose, N.K.,,,A simple general proof of Kharitonov's generalized stability criterion,IEEE Trans. Circuits and Systems,34,,,1987,1233,1237,Proves that stability of interval polynomials depends on that of 8 extreme ones.,1,0,

,11,0,0,0,0,0,Ackerman, J.E.,Barmish, B.R.,,Robust Schur stability of a polytope of polynomials,IEEE Trans. Automat. Control,33,,,1988,984,986,,1,0,

,13,0,0,0,0,0,Bortolotti, E.,,,Influenza dell'opera matematica di Paolo Ruffini sullo svolgimento delle teorie algebriche,,,,Modena,1903,0,0,,1,0,

,19,0,0,0,0,0,Saliba, G.,,,The meaning of al-jabr wa'l-muqabalah,Centaurus,17,,,1972,189,204,Vague treatment of quadratic,1,0,

,2,0,0,0,0,0,Goldstein. A.,,,Constructive Real Analysis,,,Harper & Row,,1967,0,0,Advanced treatment of Newton,1,0,

,2,14,16,0,0,0,Noble, B.,,,Numerical Methods,,,Oliver & Boyd,,1966,0,0,Treats Newton, Bairstow, errors,1,0,

,2,7,16,0,0,0,Hammerlin, G.,Hoffmann, K.H.,,Numerical Mathematics, transl. L. Schumacher,,,Springer,,1991,0,0,Treats Newton, Secant and convergence briefly,1,0,

,2,4,7,17,14,11,Zurmuhl, R.,,,Praktische Mathematik für Ingenieure und Physiker,,,Springer,,1963,0,0,Treats Newton, Secant, Graeffe, Bairstow, evaluation, stability, cubic and quartics.,1,0,

,25,0,0,0,0,0,Klein, F.,,,Vorlesungen über die Entwicklung der Mathematik in 19 Jahrhundert. Band I,,,,Berlin,1926,0,0,Some Galois theory,1,0,

,1,2,7,15,0,0,Johnston, R.L.,,,Numerical Methods a Software Approach,,,John Wiley & Sons, Inc.,New York,1982,0,0,Treats Bisection, Newton, Secant, Muller and hybrid methods; Laguerre.,1,0,

,25,0,0,0,0,0,Verriest G.,,,Leçons sur la théorie des équations selon Galois.,,,Gauthier Villars,Paris,1939,0,0,Considers conditions for solubility by radicals.,1,0,

,25,0,0,0,0,0,Verriest G.,,,Oeuvres mathématiques d'E. Galois publiées en 1897, suivies d'une notice sur E.Galois et la théorie des équations algébriques,,,Gauthier Villars,Paris,1951,0,0,Considers conditions for solubility by radicals.,1,0,

,11,0,0,0,0,0,Cieslik J.,,,On possiblities of the extension of Kharitonov's stability test for interval polynomials to the discrete time case.,IEEE Trans. Automat. Control,32,,,1987,237,238,Kharatinov test for interval polynomials does not extend to discrete time case, unless n ≤ 2,1,0,

,11,0,0,0,0,0,Wei K.W.,Yedavalli R.K.,,Invariance of strict Hurwitz property for uncertain polynomials with dependent coefficients.,IEEE Trans. Automat. Control,32,,,1987,907,909,Title says it.,1,0,

,11,0,0,0,0,0,Lipatov A.V.,Sokolov N.I.,,Some sufficient conditions for stability and instability of continuous linear stationary systems.,Autom. Remote Control,39,,,1979,1285,1291,Conditions satisfied by adjacent coefficients of characteristic polynomial,1,0,

,11,0,0,0,0,0,Soh C.B.,Berger C.S.,Dabke K.P.,Addendum to "On the stability properties of polynomials with perturbed coefficients",IEEE Trans. Automat. Control,32,,,1987,239,240,No note.,1,0,

,19,0,0,0,0,0,Lambo Ch. S.J.,,,Une algèbre française de 1484. Nicolas Chuquet,Revue Ques. Scient. (3),2,,,1902,442,472,Treats quadratic.,1,0,

,19,0,0,0,0,0,Bruins E.M.,,,Aperçu sur les mathématiques Babyloniennes,Revue d'Historie des Sciences,3,,,1950,301,314,Babylonians solved quadratic.,1,0,

,19,25,0,0,0,0,Franci R.,Rigatelli L.T.,,Storia della teoria delle equazioni algebriche.,,,,Mursia,1979,0,0,History of low-degree polynomials and existence, solution by radicals.,1,0,

,19,0,0,0,0,0,Vogel K.,,,Bemerkungen zu den quadratischen Gleichungen der babylonischen mathematik.,Osiris,1,,,1936,703,717,Quadratics in Babylonia.,1,0,

,21,0,0,0,0,0,Forrester P.J.,Rogers J.B.,,Electrostatics and the zeros of the classical orthogonal polynomials,SIAM J. Math. Anal.,17,,,1986,461,468,Electrostatic problems solved in terms of zeros of Jacobi polynomials, etc.,1,0,

,19,0,0,0,0,0,Sarton G.,,,A History of Science,,,Harvard Univ. Press,Cambridge, Mass.,1952,0,0,Sumerians solved quadratics and perhaps cubics.,1,0,

,10,0,0,0,0,0,Loria G.,,,Charles Sturm et son oeuvre mathématique,Enseign. Math. Ser. 1,37,,,1938,249,274,Brief treatment of Sturm's Theorem.,1,0,

,13,0,0,0,0,0,Schur J.,,,Zwei Sätze über algebraische Gleichungen mit lauter reelen Wurzeln,J. Reine Angrew. Math.,144,,,1914,75,88,Considers roots of products of 2 polynomials with real roots.,1,0,

,1,2,7,17,0,0,Scraton,,,Basic Numerical Methods: Intoduction to Numerical Mathematics on a Microcomputer,,,,,0,0,0,Treats Bisection, Secant, Newton, and evalutation.,1,0,

,19,0,0,0,0,0,Juschkewitsch A.P.,,,Geschichte der Mathematik im Mittelalter.,,,Teubner,Leipzig,1964,0,0,Touches on quadratic and cubic among Arabs, etc.,1,0,

,2,10,19,25,20,0,Severi F.,,,Lezioni di analisi I,,,Zanichelli,,1933,0,0,Covers Newton, Resultants, low-degree, existence, and rational coefficients.,1,0,

,20,0,0,0,0,0,Lee, T.C.Y.,Vanstone, S.A.,,Subspaces and polynomial factorizations over finite fields,Appl. Alg. Eng. Comm. Comput.,6,,,1995,147,157,No note.,1,0,

,19,0,0,0,0,0,Bortolotti, E.,,,Storia della matematica elementare, in "Enciclopedia delle matematiche elementari e complementi", Vol.3 Pt.2,,,,Milan,1950,539,750,Treats quadratic and cubic.,1,0,

,19,0,0,0,0,0,Loria, G.,,,Storia della Matematiche dall'alba della civiltà al secolo XIX,,,,Milano,1950,0,0,Treats quadratic and cubic.,1,0,

,19,0,0,0,0,0,Washington, A.J.,,,Basic Technical Mathematics with Calculus,,,Cummings,Menlo Pk, CA,1970,0,0,A good treatment of quadratic.,1,0,

,25,0,0,0,0,0,Dickson, L.E.,Börger, R.,,The Galois group of a reciprocal quartic equation,Amer. Math Monthly,15,,,1908,85,87,Gives information about solubility by radicals.,1,0,

,25,0,0,0,0,0,Börger, R.,,,On de Moivre's quintic,Amer. Math. Monthly,15,,,1908,171,174,Soluble by radicals,1,0,

,25,0,0,0,0,0,Miller,Blichfeldt,Dickson, L.E.,The points of inflexion of a plane cubic curve.,Ann. Math.,16,,,1914,50,66,Leads to 9th degree equation which is soluble by radicals.,1,0,

,21,0,0,0,0,0,Tricomi, F.G.,,,Sugli zeri dei polinomi sferici ed ultrasferici,Ann. Mat. Pur. Appl.,31,,,1950,93,97,,1,0,

,25,0,0,0,0,0,Bourgne, R.,Azra, J.-P. (eds),,Écris et mémoires mathématiques d'Evariste Galois,,,,,1962,0,0,,1,0,

,19,29,0,0,0,0,Dedron, P.,Itard, J.,,Mathematics and Mathematicians,,,Open Univ Press,Milton Keynes, Eng.,1973,0,0,Treats square roots, quadratics.,1,0,

,25,0,0,0,0,0,Galois, E.,,,Oeuvres mathématique d'Evariste Galois,J. Math. Pures Appl.,11,,,1846,381,444,Includes work on solution by radicals.,1,0,

,19,0,0,0,0,0,Hermite, C.,,,Considerations sur la résolution algébrique de l'équation du cinquème degré.,Nouv. Ann. Math.,1,,,1842,329,336,,1,0,

,13,0,0,0,0,0,Hoe, J.,,,Les Systèmes d'équations polynômes dans le siyuan yujian (1303),.,,Inst. Hautes Etudes Chin.,,0,0,0,Derives several high-order equations & solves by Horner's method.,1,0,

,19,0,0,0,0,0,Ruska, J.,,,Zur altesten arabischen algebre und rechenkust,Sitz.Heidelberger Akad. Wiss. Phil.-Hist Kl.,8 Abt. 2,,,1917,0,0,Arabic quadratics.,1,0,

,1,2,0,0,0,0,Akl, S.G.,,,The Design and Analysis of Parallel Algorithms,,,Prentice-Hall,Englewood Cliffs,1989,0,0,Parallel Bisection and Newton,1,0,

,20,0,0,0,0,0,Adleman, L.M.,Manders, K.,Miller, G.,On taking roots in finite fields, in "Proc. 18th Ann. IEEE Symp. Founds. Comp. Sci.",,,IEEE Comp. Sci. Press,CA, USA,1977,175,178,Treats quadratic residues,1,0,

,13,29,0,0,0,0,Dakhel, A.K.,,,Al-Kashi on Root extraction, ed W.A. Mijab & E.S. Kennedy,,,American Univ.,Beirut,1960,0,0,Describes Ruffini-Horner method of solving polynomials, and Arabic method for surds.,1,0,

,20,0,0,0,0,0,Panario, D.,Viola, A.,,Analysis of Rabin's Poly. Irreducibility test, in "Proc. Latin '98:Theoretical Informatics" ed C.L. Luccesi,,,Springer,,1998,0,0,,1,0,

,19,0,0,0,0,0,Sayili, A.,,,Logical Necessities in Mixed equations by Hamid ibn Turk and the Algebra of his time,,,,Ankara,1962,0,0,Detailed treatment of quadratic among Arabs,1,0,

,19,0,0,0,0,0,Ritter, F.,,,Francois Viéte, inventeur de l'algèbre moderne. Notice sur sa vie et son oeuvre.,,,,Paris,1895,0,0,Treats some low degree equations.,1,0,

,25,0,0,0,0,0,Klein, F.,,,Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert,,,,Berlin,1956,0,0,Brief treatment of fundamental theorem of algebra,1,0,

,21,0,0,0,0,0,Case, K.M.,,,Sum Rules for Zeroes of Polynomials II,J. Math. Phys.,21,,,1980,709,714,Refers to polynomials which satisfy differential equations with polynomial coefficients.,1,0,

,1,2,0,0,0,0,Costabile, F.,Gualtieri, M.I.,Luceri, R.,A New Iterative Method for the Computation of the Solution of Nonlinear Equations,Numer. Alg.,28,,,2001,87,100,Combines bisection & Newton to give a globally convergent method of order 1+ $\sqrt{2}$ ,1,0,

,19,0,0,0,0,0,Kloyda, T.,,,Linear & Quadratic Equations 1550-1650,,,Edwards,Ann Arbor,1938,,,Includes detailed history of quadratic.,1,0,

,2,7,15,24,29,1,Grove, W.E.,,,Brief Numerical Methods,,,Prentice-Hall,Englewood Cliffs,NJ,1966,0,0,Treats bisection, Newton, secant, Muller, Halley,acceleration, square root.,1,0,

,19,0,0,0,0,0,Gullberg, J.,,,Mathematics from the birth of numbers,,,Norton,New York,1997,0,0,Treats low-degree equations in detail, including history.,1,0,

,20,0,0,0,0,0,Dedekind, R.,,,Abriss einer Theorie der höheren Kongruenzen in bezug auf einen reelen Primzahl-Modulus,J. Reine Angew. Math.,54,,,1857,1,26,Treats high-degree congruences,1,0,

,20,0,0,0,0,0,Dedekind, E.,,,Beweis für die Irreduktibilitat der Kreisteilungs-Gleichung,J. Reine Angew. Math,54,,,1857,27,30,Treats high-degree congruences.,1,0,

,11,0,0,0,0,0,Chapellat, H.,Dahleh, M.,Bhattacharyya, S.P.,Robust stability under structured and unstructured perturbations,IEEE Trans. Automat. Contr.,35,,,1990,1100,1108,,1,0,

,11,0,0,0,0,0,Minnichelli, R.J.,Anagnost, J.J.,Desoer, C.A.,An elementary proof of Kharitonov's theorem with extensions.,IEEE Trans. Automat. Control,34,,,1989,995,998,Whole class of polys stable if 4 special ones are. New Proof.,1,0,

,11,0,0,0,0,0,Rantzer, A.,,,Hurwitz testing sets for parallel polytopes of polynomials.,Systems Control Lett.,15,,,1990,99,104,,1,0,

,2,15,0,0,0,0,Palacias, M.,,,Kepler equation and accelerated Newton method.,J. Comput Appl. Math,138,,,2002,335,346,Generalized Newton method. Order 3 version most efficient.,1,0,

,1,5,0,0,0,0,Dellnitz, M.,Schütze, O.,Zheng, Q.,Locating all the zeros of an analytic function in one complex variable,J. Comput. Appl. Math.,138,,,2002,325,333,Adaptive mutli-level algorithm based on argument principle.,1,0,

,19,13,0,0,0,0,Mikami, Y.,,,Scientific Japan, Past & Present, J. Sakurai (ed),,,,,1926,177,198,Brief mention of quadratics etc.,1,0,

,19,29,0,0,0,0,Resnikoff, H.L.,Wells Jr., R.O.,,Mathmatics in Civilization,,,Dover,New York,1984,0,0,Babylonian surds and quadratics,1,0,

,19,0,0,0,0,0,Stillwell, J.,,,Mathematics and its History,,,Springer,New York,1989,0,0,Solution of quadratic and cubic,1,0,

,19,25,0,0,0,0,Dunham, W.,,,Journey through Genius,,,John Wiley & Sons,New York,1990,0,0,Good treatment of cubic, solution by radicals,1,0,

,19,0,0,0,0,0,Hooper, A.,,,The River Mathematics,,,Henry Holt & Co.,New York,1945,0,0,Good treatment of quadratic,1,0,

,25,0,0,0,0,0,Bachmacova, I.,,,Le théorème fondamental de l'Algèbre et la construction des corps algébriques,Archives Internat. D'hist. Des Sciences,13,,,1960,211,222,Detailed history of fundamental theorem of algebra,1,0,

,21,0,0,0,0,0,Laforgia, A,Siafarikas, P.,,Inequalities for the zeros of ultraspherical polynomials, in "Orthogonal Polynomials and Their Applications", ed. C. Brezinski et al,,,Baltzer,Basel,1991,327,330,,1,0,

,21,0,0,0,0,0,Recchioni, M.C.,,,Quadratically convergent method for simultaneously approaching the roots of polynomial solutions of a class of diffferential equations: Applic's to Orthogonal Polynomials,Numer. Alg.,28,,,2001,285,308,,1,0,

,19,0,0,0,0,0,Thompson, J.E.,,,Algebra for the Practical Worker,,,Van Nostrand Reinhold,New York,1982,0,0,Good treatment of quadratic, cubic and quartic.,1,0,

,11,0,0,0,0,0,Petersen, I.R.,,,Extensions to Kharitonov's Theorem, in "Proc. Ist Int. Symp. Sig. Proc. Appls",,,,,0,83,88,,1,0,

,10,4,19,25,0,0,Sansone, G.,Conti, R.,,Lezioni di analisi matematica,,,Cedam,Padova,1958,0,0,Treats Graffe, Sturm. Low degree and existence.,1,0,

,25,0,0,0,0,0,Betti, E.,,,Sulla risoluzione dell'equazione algebriche,Ann. Sci. Mat. Fis,3,,,0,49,115,Treats solution by radicals,1,0,

,17,0,0,0,0,0,Heinrich, H.,,,Einführung in die Praktische Analysis,,,Mayer,Aachen,1963,0,0,Horner's methof for evaluation,1,0,

,19,0,0,0,0,0,Howe, G.,,,Mathematics for the Practical Man,,,Van Nostrand,Princeton,1957,0,0,Simple treatment of quadratic.,1,0,

,20,0,0,0,0,0,Gauss, C.F.,,,Untersuchungen über höhere Arithmetik,,,,Berlin,1889,0,0,Treats congruences.,1,0,

,25,0,0,0,0,0,Gauss, G.F.,,,Die vier Gauss'schen Beweise für die Zerlegung ganzer algebraischer Functionen in reele Factoren ersten oder zweiten Grades (1799-1849),Ostwald's Klassiker,14,,Leipzig,1890,0,0,Proofs of existence,1,0,

,2,4,6,10,25,19,Nicolletti, O.,,,Proprietà generali delle equazioni algebriche,Encycl. Mat. Elementari,1, pt2,Hoepli,Milano,1962,201,322,Covers Newton, Graeffe, Bernouilli, solution by radicals, existence, low-degree.,1,0,

,19,0,0,0,0,0,Togliatti, E.G.,,,Equazioni di secondo, terzo, quarto grado ed altre equazioni algebriche particolari, Sistemi di equazioni algebriche di tipo elementare,Encycl. Mat. Elemtari,,,,1964,265,231,Thorough treatment of low-degree and other special cases.,1,0,

,11,0,0,0,0,0,Barmish, B.R.,,,New tools for robustness analysis, in "Proc. 27th IEEE Conf. Decision Control",,,,,1988,1,6,Surveys applications of Kharitonov's theorem,1,0,

,11,0,0,0,0,0,Fu, M.,Barmish, B.R.,,Maximal unidirectional perturbation bounds for stability of polynomials and matrices.,Syst Control Lett.,11,,,1988,173,179,Bounds perturbations which preserve stability,1,0,

,11,0,0,0,0,0,Tesi, A.,Vicino, A.,,Robustness analysis for uncertain dynamical systems with structured perturbations, in "Proc. IEEE CDC",,,,,1988,519,525,Considers stability of families of polynomials.,1,0,

,19,0,0,0,0,0,Eves H.,,,An Introduction to the History of Mathematics,,,Holt, Rinehart,New York,1969,0,0,Treats history up to quartics,1,0,

,19,0,0,0,0,0,Gandz S.,,,"A Few Notes on Egyptian and Babylonian Mathematics" in Studies and Essays in the History of Science and Learning: Offered in Homage to George Sarton on the Occasion of his Sixtieth Birthday,,,Henry Schumann,New York,1944,449,462,Brief mention of quadratics,1,0,

,11,0,0,0,0,0,Dasgupta S.,,,Kharitonov's theroem revisited,Syst Control Lett.,11,,,1988,381,384,All members of a family are stable if 4 extreme members are,1,0,

,11,0,0,0,0,0,Foo Y.K.,Soh Y.C.,,Stability of a family of polynomials with coefficients bounded in a diamond,IEEE Trans. Automat. Control,AC-36,,,1991,1501,1502,Title says it.,1,0,

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,19,0,0,0,0,0,Sayili A,,,The Algebra of Ibn Turk,,,,Ankara,1985,0,0,Early treatment of quadratic,1,0,

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,19,0,0,0,0,0,Barbarin P,,,Les fonctions hyperboliques dans l'enseignment moyen,Enseign. Math,2,,,1900,443,447,Solves cubic in terms of hyperbolic functions,1,0,

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,19,0,0,0,0,0,Gundelfinger S,,,Bemerkung zur Auflosung der cubischen Gleichungen,Math. Ann.,3,,,1871,272,275,,1,0,

,13,0,0,0,0,0,Abel N.H.,,,Mémoire sur une classe particulière d'équations résolubles algébriquement,Oeuvres,,,,1881,478,507,,1,0,

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,19,0,0,0,0,0,Hellman M.J.,,,A unifying technique for the solution of the quadratic, cubic, and quartic,Amer. Math. Monthly,65,,,1959,274,276,Title says it,1,0,

,20,0,0,0,0,0,Ore O,,,Contributions to the theory of finite fields,Trans. Amer. Math. Soc.,36,,,1934,243,274,Higher congruences,1,0,

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,19,0,0,0,0,0,Cayley,,,On a new auxiliary equation in the theory of equations of the fifth order, in "Collected Mathematical Papers" Vol. 4,,,,Cambridge,1891,309,324,,1,0,

,19,29,0,0,0,0,Yan Li,Shiran Du,,Chinese Mathematics- A Concise History (translated by J.N. Crossley and A.W.C. Lun),,,Claredon Press,Oxford,1987,0,0,Treats surds and whether polys have positive roots,1,0,

,19,29,0,0,0,0,Swetz F,Se Ang Tian,,A brief chronological and bibliographic guide to the history of Chinese mathematics,Historia Mathematica,11,,,1984,39,56,Includes brief history of low degree equations in China,1,0,

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,19,0,0,0,0,0,Bourbaki N,,,Eléments d'histoire des mathématiques,,,Hermann,Paris,1974,0,0,Treats cubic solution,1,0,

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,19,29,0,0,0,0,Robert of Chester,,,Latin Translation of al-Khwarizmi's Al-Jabr ed. by Barnabus Hughes,,,Stiener Verlag Wiesbaden,Stuttgart,1989,0,0,Treats quadratic and square roots by Arabs,1,0,

,17,0,0,0,0,0,Ceberio M,Granvilliers L.,,Horner's Rule for Interval Evaluation revisited,Computing,69,,,2002,51,81,Interval evaluation improved by 25%,1,0,

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,19,0,0,0,0,0,Tartinville A,,,Théorie des équations et des inéquations du premier et du second degré a une inconnue,,,Nony & Co.,Paris,1902,0,0,Thorough treatment of quadratics,1,0,

,21,0,0,0,0,0,Alvarez-Nodarse R,Dehesa J.S.,,Distribution of zeros of discrete and continuous polynomials from their recurrence relation,Appl. Math. Comput.,128,,,2002,167,190,Treats classical orthogonal polynomial systems,1,0,

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,11,0,0,0,0,0,Barmish B.R.,,,Invariance of the strict Hurwitz property for polynomials with perturbations, in "IEEE Conf. On Decision and Control",,,,San Antonio,1983,353,355,Exploits Kharitonov's theorem,1,0,

,11,0,0,0,0,0,Frazer R.A.,Duncan W.J.,,On the criteria for stability for small motions,Proc. Royal Soc.,A-124,,,1929,642,654,Gives conditions for stability,1,0,

,19,0,0,0,0,0,Godt W,,,über den sogennanter irreduzibelen Fall der kubischen Gleischungen,Arch. Math. Phys. (Ser. 3),9,,,1905,213,214,,1,0,

,19,0,0,0,0,0,Jacobi C.G.J.,,,Observatiunculae ad theoriam aequationum pertinentes,J. Reine Ang. Math.,13,,,1835,340,352,Considers degrees up to the sixth,1,0,

,19,0,0,0,0,0,Lodge A,,,On the solution of the general equation of the fourth degree,Quart. J. Math.,19,,,1883,257,262,,1,0,

,10,0,0,0,0,0,Mignosi G,,,Teorema di Sturm e sue estensioni,Rend. Circ. Mat. Palermo,49,,,1925,1,164,,1,0,

,7,0,0,0,0,0,Mammana G.,,,Lemma fondamentale per il calcolo approssimato delle radici di una equazione,Rend. Circ. Mat. Palermo,47,,,1923,109,114,Treats Secant method,1,0,

,7,0,0,0,0,0,Allara E,,,A propisito di una metodo di approssimazione degli zeri di una funzione,Rend. Circ. Mat. Palermo,49,,,1925,387,392,Treats Secant Method,1,0,

,19,0,0,0,0,0,Godman A,Talbert J.F.,,Additional Mathematics- Pure and Applied,,,Longman,London,1971,0,0,Good treatment of quadratic,1,0,

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,19,0,0,0,0,0,Seidelmann F,,,Die Gesamtheit der kubischen und biquadratischen Gleichungen,Math. Ann.,78,,,1918,230,233,,1,0,

,19,0,0,0,0,0,Kummer E.E.,,,Ueber die cubischen und biquadratischen Gleichungen,Monatsber. Akad. Berlin,,,,1880,930,936,,1,0,

,19,0,0,0,0,0,Réalis S,,,Simples remarques sur les racines entières des équations cubiques,Nouv. Ann. Math. (ser. 2),14,,,1875,289,298,Also pp 424-427,1,0,

,19,0,0,0,0,0,André D,,,Sur l'équation du troisième degré,Nouv. Ann. Math. (Ser. 2),14,,,1875,356,358,,1,0,

,19,0,0,0,0,0,Borden J,,,Question 1229,Analyst,5,,,1878,110,112,,1,0,

,19,25,0,0,0,0,Muir J,,,Of Men and Numbers: The Story of the Great Mathematicians,,,Dodd, Mead,New York,1961,0,0,Cursory treatment of cubic & existence,1,0,

,19,20,25,0,0,0,Haupt O,,,Einführung in die Algebra vol 1,,,,Leipzig,1929,0,0,Treats existence, low degree,1,0,

,20,0,0,0,0,0,Adleman L.M.,Manders K,Miller G,On taking roots in finite fields,Proc. 18th Ann. IEEE Sym. On Found. of Comp. Sci.,,IEEE Computer Soc. Press,California, USA,1977,175,178,Treats quadratic residues,1,0,

,19,0,0,0,0,0,Schuster H.S.,,,Quadratische Gleichungen der Seleukdenzeit aus Uruk,Quel. Stud. Gesch. Math.,B-1,,,1930,194,200,,1,0,

,19,0,0,0,0,0,Starkweather G.P.,,,A solution to the biquadratic by binomial resolvents,Bull. Amer. Math. Soc. (Ser. 2),4,,,1898,524,528,,1,0,

,19,0,0,0,0,0,Dixon T.S.E.,,,A new solution of biquadratic equations,Amer. J. Math.,1,,,1878,283,284,Allegedly easier than classical method,1,0,

,25,0,0,0,0,0,Novy L,,,Origins of Modern Algebra,,,Noordhoff,Groningen,1973,0,0,Treats solubility of equations,1,0,

,25,0,0,0,0,0,Schaaf W.L.,,,Carl Freidrich Gauss,,,Watts,New York,1964,0,0,Popular history of existence theorem,1,0,

,19,0,0,0,0,0,Kummel H,,,To express the roots of the solvable quanitities as symmetrical functions of Homologues,Amer. J. Math.,18,,,1896,74,94,Degrees up to 4th.,1,0,

,19,0,0,0,0,0,Cayley A,,,Note on a cubic equation, in "Collected Math. Papers",,,Cambridge University Prs,Cambridge,1897,421,423,,1,0,

,19,0,0,0,0,0,Pleskot A,,,Nouveau procédé pour résoudre les équations du trosieme degré,Nouv. Ann. Math.Ser. 3,18,,,1899,65,66,,1,0,

,19,0,0,0,0,0,McClintock E,,,A simplified solution of the cubic,Ann. Math. Ser. 2,2,,,1901,151,152,,1,0,

,19,0,0,0,0,0,Procissi A,,,Il caso irriducibile della equazione cubica da Cardano,Period. Mat. Ser. 4,29,,,1951,263,280,Thorough historical treatment of cubic,1,0,

,19,0,0,0,0,0,Valeriani V,,,Suluzione analitice delle equazioni biquadratiche complete,Giorn. Mat.,13,,,1875,99,106,Solves quartic,1,0,

,13,0,0,0,0,0,Antomari X,,,Sur les conditions qui expriment qu'une équation de degré m n'a que p racines destinct,Nouv. Ann. Math.Ser 3,16,,,1897,63,75,,1,0,

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,19,0,0,0,0,0,Janni V,,,Supra una formola di Arnhold,Giorn. Mat.,21,,,1883,213,216,Treats quartic,1,0,

,28,0,0,0,0,0,Rados G,,,Sur la théorie des racines de l'unité,Rend. Circ. Mat. Palermo,36,,,1913,299,304,,1,0,

,21,0,0,0,0,0,Cipolla M.,,,Sulle equazioni algebriche le cui radici sono tutte radici dell' unita,Rend. Circ. Mat.Palermo,38,,,1914,370,375,,1,0,

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,29,0,0,0,0,0,Phillips G.M.,Taylor P.J.,,Computers,,,Methuen,London,1969,0,0,Treats bisection and Newton's method as applied to square roots.,1,0,

,11,0,0,0,0,0,Milanese M et al (eds),,,Proc. Intern. Workshop on Robustness in Identification and Control p.95, 123, 144, 181,,,Plenum,New York,1989,0,0,Several papers on stability of polynomials with perturbed coefficients,1,0,

,5,0,0,0,0,0,Kravanja P,van Barel M,,Computing the Zeros of Analytic Functions,,,Springer-Verlag,Berlin,2000,0,0,Mostly integration methods,1,0,

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,20,0,0,0,0,0,Fleischmann P.,Holder M. Chr.,,The black-box Niederreiter algorithm and its implementation over the binary field,Math. Comp.,72,,,2003,1887,1899,Factorization of high-degree polynomials over binary field. Includes parallel program.,1,0,

,20,0,0,0,0,0,Wang P.S.,,,Symbolic Computation and Parallel Software, in "Parallel Computation", ed. H.P. Zima,,,,,1991,316,337,Treats factorization over integers,1,0,

,2,10,19,25,0,0,Archibald R.C.,,,Outline of the History of Mathematics (no.2 of the Herbert Ellsworth Slaught Memorial Papers),Amer. Math. Monthly,56, No.1 Pt.2,,,1949,1,114,Historical treatment of low degree, Newton, Sturm, existence, etc.,1,0,

,19,0,0,0,0,0,Pellet A.E.,,,Sur l'équation du quatrième degré et les fonctions elliptiques.,Bull. Soc. Math. France,14,,,1886,90,93,,1,0,

,19,0,0,0,0,0,Darbi G,,,Sulle equazioni di 4e Grado,Giorn. Math.,38,,,1990,153,164,Treats quartic,1,0,

,19,0,0,0,0,0,Briot F,,,Résolution de l'équation du quatrième degré,Nouv. Ann. Math. Ser. 2,20,,,1881,225,227,Solves quartic,1,0,

,19,0,0,0,0,0,Perrin R,,,Sur une nouvelle méthode de résolution de l'équation du quatrième degré, et son application á quelques équations de degrés superieurs,Bull. Soc. Math. France,10,,,1882,139,146,Solves quartic and some higher order equations,1,0,

,19,0,0,0,0,0,Lucas F,,,Nature des racines de l'équations du quatrième degré,Bull. Soc. Math France,18,,,1890,145,149,Considers quartic,1,0,

,25,0,0,0,0,0,Abel N.H.,,,Mémoire sur les équations algébriques, ou l'on démontre l'impossibilité de la résolution de l'équation généal du cinquième degré,Oeuvres complete,1,,,1824,28,33,Impossibility of solution by radicals for degrees >4,1,0,

,25,0,0,0,0,0,Abel N.H.,,,Démonstration de l'impossibilité de la résolution algébrique des équation générales qui passent le quatrième degré,Oeuvres complete,1,,,1826,66,87,Impossibility of solution by radicals for degrees >4,1,0,

,21,0,0,0,0,0,Abel N.H.,,,Abhandlung über eine besondere Klasse algebraisch auflösbarer Gleichungen,Ostwald's Klassiker,111,,Leipzig,1900,1,50,Deals with xⁿ-1=0,1,0,

,11,10,19,25,2,7,Aleksandrov A.D. et al,,,Mathematics: Its Content, Methods, and Meaning. 3 vols.,,,MIT Press,Cambridge, Mass.,1965,0,0,Brief treatment of low-degree, existence, Sturm, Hurwitz, Newton, Secant, and Graeffe's methods.,1,0,

,11,0,0,0,0,0,Aleksandrov A.D.,Nikolaev Yu.P.,,The subspace of asymptotical stability of a class of linear stationary systems,Autom. Remote Control,35,,,1974,521,528,,1,0,

,2,7,17,0,0,0,Ketter R.L.,Prawel S.P. jr.,,Modern Methods of Engineering Computation,,,McGraw-Hill Book Co.,New York,1969,0,0,Treats Newton, reguli falsi, evaluation,1,0,

,1,2,7,19,14,16,LaFara R.L.,,,Computer Methods for Science and Engineering,,,Hayden Book Co.,Rochelle Park, N.J.,1973,0,0,Treats bisection, Newton, Secant, Lin, convergence, and low degree.,1,0,

,19,0,0,0,0,0,Levi H,,,Elements of Algebra,,,Chelsea,New York,1962,0,0,Simple treatment of quadratic.,1,0,

,19,0,0,0,0,0,Lumpkin B,,,A mathematics club project from Omar Khayyam,Math. Teacher,71,,,1978,740,744,Geometric solution of cubic,1,0,

,22,0,0,0,0,0,Rouillier F,Zimmermann P,,"Efficient isolation of polymonials' real roots",J. Comput. Appl. Math.,162,,,2004,33,50,Uses Vincent-Akritas method with multiple-precision interval arithmetic. Works up to degree 1000 or more.,1,0,

,19,0,0,0,0,0,Berggren L. J.,,,Innovation and tradition in Sharaf al-Din al-Tusi's al Mu'adalat,Journal of the American Oriental Society,110,,,1990,304,309,Treats conditions for existence of roots of cubic, etc.,1,0,

,19,0,0,0,0,0,Hogendijk J.P.,,,Sharaf al-Din al-Tusi on the number of positive roots of cubic equations,Historia Mathematica,16,,,1989,69,85,Uses geometric methods to find roots of cubic,1,0,

,19,0,0,0,0,0,Rashed R,,,Sharaf al-Din al-Tusi, oeuvres mathématiques: Algèbre et géométrie au XII siècle,,,S.E.B.L.,Paris,1986,0,0,Adhoc method for cubic,1,0,

,19,0,0,0,0,0,King D.A. (ed),Kennedy M.H. (ed),,Studies in the Islamic Exact Sciences,,,Amer. Univ Of Beirut Pr.,Beirut,1983,0,0,Brief treatment of quadratic and cubic by Arabs,1,0,

,19,0,0,0,0,0,Hoyrup J,,,The formation of 'Islamic Mathematics': sources and conditions,Science in Context,1,,,1987,281,329,Historical/philosophical discussion of early solution of quadratic,1,0,

,11,0,0,0,0,0,Ghosh B.K.,,,Some new results on the simultaneous stabilizability of a family of single input, single output systems,Systems Control Lett.,6,,,1985,39,45,,1,0,

,11,0,0,0,0,0,Yeung K.S.,,,Linear system stability under parameter uncertainties,Internat. J. Control,38-2,,,1983,459,464,,1,0,

,11,0,0,0,0,0,Lin H,Hollot C.V.,Bartlett A.C.,Stability of families of polynomials: geometric considerations in coefficient space.,Internat. J. Control,45,,,1987,649,660,,1,0,

,4,,,,,,Aleksandrov A.D. et al,,,Mathematics: Its Content, Methods, and Meaning. 3 vols.,,,MIT Press,Cambridge, Mass.,1965,0,0,Brief treatment of low-degree, existence, Sturm, Hurwitz, Newton, Secant, and Graeffe's methods.,1,0,

,14,,,,,,Isaacson E,Keller H.B.,,Anaylsis of Numerical Methods,,,John Wiley and Sons,New York,1966,0,0,Treats Newton, Secant, Bernoulli, Sturm, Bairstow, evaluation, and acceleration.,1,0,

,21,0,0,0,0,0,Méray C.,,,Démonstration analytique … des racines des équations binomes,Ann. Ecole Norm Ser. 3,2,,,1885,337,356,Roots of xⁿ = a,1,0,

,19,0,0,0,0,0,Becker O.,,,Grundlagen der Mathematik in geschichtlicher Entwicklung,,,Alber,Freiburg,1954,0,0,Babylonian treatment of quadratic,1,0,

,2,4,6,0,0,0,Nicoletti O.,,,Proprieta generali delle Equazioni Algebriche: IV: Metodi di approssimazione, in "Enciclopedia delle Mat.", ed Berzolari L et al,,1 Pt 2,Hoepli,Milano,1932,236,248,Treats Newton, Graeffe, Bernoulli,1,0,

,19,0,0,0,0,0,Am Ende H,,,Ueber eine die gleichungen zweiten, dritten und vierten grades umfessande auflösungsmethode,Arch. Math. Phys. Ser. 2,3,,,1885,103,106,Treats degree 2-4,1,0,

,19,0,0,0,0,0,Archibald R.C.,,,Notes on Omar Khayyam (1050-1122),Pi mu Epsilon Journal,1,,,1953,351,358,Very brief discussion of cubics according to Arabs.,1,0,

,19,0,0,0,0,0,Amighi G.,,,Note di algebra di Pierro della Francesa,Physis,11,,,1967,421,424,Treats low degrees.,1,0,

,19,0,0,0,0,0,Artom,,,Le equazioni di secondo grado presso I Greci,Period. Mat. Ser. 4,2,,,1922,326,342,History of quadratic among Greeks.,1,0,

,11,0,0,0,0,0,Bartlett A.C.,Hollot, C.V.,Lin, H.,Root locations of an entire polytope of polynomials: it suffices to check the edges,Math. Of Control, Signals, and Systems,1,,,1988,61,71,,1,0,

,10,0,0,0,0,0,Björling C.F.E.,,,Sur la réalité des Racines d'équations algébriques.,Arch. Math. Phys.,48,,,1868,363,375,,1,0,

,19,0,0,0,0,0,Candido G.,,,La risoluzioni della equazione di quarto grado,Period. Mat. Ser. 4,21,,,1942,21,44,History of quartic,1,0,

,19,0,0,0,0,0,Candido G.,,,Le risoluzioni della equazione di quarto grado: fagnano,Period. Mat. Ser. 4,21,,,1942,151,176,Treats quartic and lower degree.,1,0,

,19,0,0,0,0,0,Candido G.,,,La risoluzioni della equazione di quarto grado: Ferrari-Eulero-Lagrange.,Period. Mat. Ser. 4,21,,,1942,88,106,History of solution of quartic,1,0,

,19,0,0,0,0,0,Carnahan W.H.,,,Geometric solutions of quadratic equations,School Sci. Math.,47,,,1947,689,690,Greek and Arabic solutions,1,0,

,19,0,0,0,0,0,Cassina,,,Sulla equazioni cubiche di Al-Biruni,Period. Mat. Ser. 4,21,,,1942,3,20,Arabic treatment of cubic,1,0,

,19,0,0,0,0,0,Carnahan W.H.,,,History of Algebra,School Sci. Math.,46,,,1946,7,12,Note: also pages 125-130. Simple history of Cardan's solution of cubic.,1,0,

,19,23,0,0,0,0,Citterio G.C.,,,Un regolo per la lettura immediata delle radici di un'equazione cubica trinoma,Period. Mat. Ser. 4,41,,,1963,272,278,A mechanical device for solving cubics,1,0,

,19,0,0,0,0,0,De Pasquale L.,,,Le equazioni di terzo grado in "quesiti et inventioni diverse di Tartaglia",Period. Mat. Ser. 4,35,,,1957,79,93,History of solution of cubic,1,0,

,13,0,0,0,0,0,Fischer F.W.,,,Einiges über Gleichungen, welche auf reciproke Gleichungen zurrückgeführt werden können,Arch. Math. Phys.,55,,,1873,294,301,,1,0,

,19,0,0,0,0,0,Franci R,,,Towards a history of algebra from Leonardo of Pisa to Luca Pacioli,Janus,72,,,1985,17,82,History of low-degree polynomials in the Middle Ages.,1,0,

,13,0,0,0,0,0,Galois E,,,Note sur la résolution des équations numériques,Bull. Univ. Sci.Indust. Sec.1,Bull. Sci.Math.Astr.,13,,,1830,413,414,,1,0,

,19,0,0,0,0,0,Gergonne M,,,Remarque sur la résolution des équations du quartième degré par la méthode de M. Wronski,Ann. Math. Pures. Appl.,3,,,1812,137,139,,1,0,

,19,0,0,0,0,0,Grassman H,,,Elementare Auflösung der allgemeinen Gleichung vierten Grades.,Arch. Math. Phys.,51,,,1870,93,96,Treats quartic,1,0,

,19,0,0,0,0,0,Grunert J.A.,,,Die allgemeine Cardanische Formel,Arch. Math. Phys.,40,,,1863,246,249,Treats Cardan's formula for cubic.,1,0,

,19,0,0,0,0,0,Hoppe R,,,Ueber transformation und numerische Lösung der kubisehen Gleichung,Arch. Math. Phys. Ser.2,13,,,1894,95,99,Treats cubic,1,0,

,19,0,0,0,0,0,Hoppe R,,,Bezirke der drei wurzelformen der Gleichung 4: grades,Arch. Math. Phys. Ser.2,14,,,1896,398,404,Treats quartic,1,0,

,19,0,0,0,0,0,Karpinski L.C.,,,The mathematics of the Orient,School. Sci. Math.,34,,,1934,467,472,Brief treatment of ancient quadratics,1,0,

,19,0,0,0,0,0,Liebrecht E,,,Ueber kubische Gleichungen,Arch. Math. Phys.,59,,,1876,217,217,Brief note about cubic,1,0,

,19,0,0,0,0,0,Liebrecht E,,,Ueber rationale Wurzeln kubischer Gleichungen in rationaler Gestalt,Arch. Math. Phys.,60,,,1877,216,218,Treats cubic,1,0,

,29,0,0,0,0,0,Gurjar L.V.,,,The value of the $\sqrt{2}$ given in the Sulvasutras,J. Univ. Bombay N.S.,10 (5),,,1942,6,10,Early calculation of sqrt (2),1,0,

,19,0,0,0,0,0,Ligowski W,,,Bermerkungen zu der in Tell 55. Seite 426 gegebenen Auflösung der Gleichungen vierten Grades.,Arch. Math. Phys.,67,,,1863,446,447,Treats quartic,1,0,

,19,0,0,0,0,0,Ligowski W,,,Zuruckfuhrung der vollstundigen Gleichung vierten Grades auf eine reciproke Gleichung zweiten Grades,Arch. Math. Phys.,65,,,1880,426,429,Studies quartics via a reciprocal quadratic.,1,0,

,19,0,0,0,0,0,Luckey P,,,Thabit ibn Qurra uber den geometrischen Richtigkeitsnachweis der auflosung der quadratischen Gleichungen,Ber. Verhand. Sach. Akad. Wiss. Leipzig Math-Phys,93,,,1941,93,114,Geometric solution of quadratic by Arabs,1,0,

,19,0,0,0,0,0,Milarch E,,,Die kubische Gleichungen,Unter. Math. Natur.,14,,,1908,30,30,Brief treatment of cubic,1,0,

,19,0,0,0,0,0,Eckhardt E.,,,Zur Auflösung der Gleichung vierten Grades,Zeit. Math. Naturwiss. Unterr.,41,,,1910,33,34,Treats quartics,1,0,

,21,0,0,0,0,0,Kim et al,,,Sobolev-type orthogonal polynomials and their zeros,Rend. Mat. Ser. 7,17,,,1997,423,444,,1,0,

,19,29,0,0,0,0,Milhaud G.,,,La géometrie d'Apastamba,Rev. Gen. Sci. Pures Appl.,21,,,1910,512,520,sqrt(2) and quadratic in early India,1,0,

,19,0,0,0,0,0,Miller G.A.,,,Marginal notes on Cajori's History of Mathematics,School Sci. Math.,19,,,1919,830,835,Brief Reference to cubics,1,0,

,19,0,0,0,0,0,Miller G.A.,,,Marginal notes on Cajori's History of Mathematics,School Sci. Math.,23,,,1923,138,149,Slight reference to low-degree and solution by radicals,1,0,

,19,0,0,0,0,0,Miller G.A.,,,Historical note on the solution of equations,School Sci. Math.,24,,,1924,509,510,Shows that solution of cubic not completed until mid-18th century,1,0,

,19,0,0,0,0,0,Natucci A.,,,Storia della teoria delle equazioni I. Dall'antichita all'inizio del secolo XVI^o,Period. Mat. Ser. 4,41,,,1963,257,271,Ancient quadratics,1,0,

,19,0,0,0,0,0,Nell A.M.,,,Ueber die allgemeine Auflösung der Gleichungen vierten Grades,Arch. Math. Phys.,56,,,1874,407,421,Treats quartics,1,0,

,3,12,0,0,0,0,Petkovic M.S.,Trickovic S.,Herceg D.,On Euler-like Methods for the Simultaneous Approximation of Polynomial Zeros,Japan J. Ind. Appl. Math.,15,,,1998,295,315,Describes a fourth-order simultaneous method, combining float and inclusion methods,1,0,

,19,25,0,0,0,0,Reves G.E.,,,Outline of the History of Algebra,School Sci. Math.,52,,,1952,63,69,Brief treatment of low degree, and existence,1,0,

,19,0,0,0,0,0,Rodet L.,,,L'Algèbre d'Al-Kharizmi,J. Asiatique Ser. 7,11,,,1878,5,98,Arabic treatment of quadratic,1,0,

,19,0,0,0,0,0,Sommer J.,,,Eine Lösung der Gleichungen vom dritten und vierten Grade vermittelst desselben Princips,Arch. Math. Phys.,27,,,1856,354,358,Treats cubic and quartic,1,0,

,13,0,0,0,0,0,Shönemann T.,,,Ueber die Beziehungen, welche zwischen den Wurzeln irreductibiler Gleichungen…,Denk. Kais. Akad. Wiss., Math.-Nat…,5,,,1853,143,156,,1,0,

,19,0,0,0,0,0,Thureau-Dangin F.,,,Notes Assyriologiques,Rev. Assyr. Archeol. Orient.,29,,,1933,136,142,Ancient treatment of quadratic,1,0,

,25,0,0,0,0,0,Vitali G.,,,Sul teorema fondamentale dell'algebra,Period. Mat. Ser. 4,8,,,1928,102,105,Treats existence,1,0,

,19,0,0,0,0,0,Vogel K.,,,Babylonische Mathematik,Bayer. Blatt. Gymn.-Schul.,71,,,1935,27,29,Ancient quadratics,1,0,

,19,0,0,0,0,0,Weltzien C.,,,Die rationale Lösung der Gleichung dritten Grades,Arch. Math. Phys. Ser. 3,28,,,1919,91,92,Brief note on cubics,1,0,

,19,0,0,0,0,0,Weltzien C.,,,Sopra una speciale classe di equazioni di terzo grado,Period. Mat. Ser. 3,9,,,1911,174,179,Treats special case of cubic,1,0,

,19,0,0,0,0,0,Thureau-Dangin F.,,,Notes Assyriologiques,Rev. Assyr. Archeol. Orient.,30,,,1933,184,188,Ancient quadratic,1,0,

,20,0,0,0,0,0,Ore O.,,,ueber die Reduzibilitat von algebraischen Gleichungen,Vid. Skrift. Math.-Nat. Kl.,??,,,1923,1,37,,1,0,

,11,0,0,0,0,0,Tsypkin Y.,Polyak B.,,Frequency criteria of linear discrete systems robust stability,Automatika,4,,,1990,3,9,,1,0,

,11,0,0,0,0,0,Polyak B.T.,Tsypkin Y. Z.,,Frequency criteria for robust stability and aperiodicity of linear systems,Autom. Remote Control,51,,,1990,1192,1200,,1,0,

,11,0,0,0,0,0,Jury E.I.,,,Discrete system robustness: a survey,Autom. Remote Control,51,,,1990,571,592,,1,0,

,13,0,0,0,0,0,Read C.B.,,,Articles on the history of Mathematics:…,School Sci. Math.,59,,,1959,689,717,Contains a bibliography: several articles on polynomials mentioned,1,0,

,19,0,0,0,0,0,Natucci,,,Storia della teoria delle equazioni,Period. Mat. Ser. 4,42,,,1964,277,290,Ancient treatment of quadratic and cubic,1,0,

,19,0,0,0,0,0,Casara G.,,,Un problema archimedeo di 3^o grado e le sue soluzioni attraverzo I tempi,Boll Unione Mat. Ital. Ser. 2,4,,,1942,244,262,Treats history of special cubic related to volume of a sphere,1,0,

,29,0,0,0,0,0,von Sanden H.,,,Quadratwurzel mit der Rechenmaschine,Zeit. Angew. Math. Mech.,38,,,1958,71,0,Square root with a calculator,1,0,

,2,4,7,17,0,0,Schultz G.,,,Formelsammlung zur praktischen Mathematik,,,,Berlin,1945,0,0,Treats Newton, Graeffe, reguli falsi, evaluation,1,0,

,2,10,14,17,19,29,Butler R.,Kerr E.,,An Introduction to Numerical Methods,,,Pitman,London,1967,0,0,Treats Newton, Descartes, Bairstow, Horner, low degree, surds,1,0,

,2,4,7,0,0,0,Redish K.A.,,,Introduction to Computational Methods,,,English University Press,,1961,0,0,Treats Newton, Graeffe, reguli falsi,1,0,

,11,0,0,0,0,0,Barmish B.R.,,,Invariance of the strict Hurwitz property for Polynomials with perturbed coefficients,IEEE Trans. Autom. Contr.,29,,,1984,935,936,,1,0,

,19,0,0,0,0,0,Struik D.J.,,,On ancient Chinese Mathematics,Math. Teacher,56,,,1963,424,0,Horner's method for quadratic discovered by Chinese,1,0,

,19,0,0,0,0,0,Terquem O.,,,'Arithmétique et algèbre des Chinois' par M.K.L. Biernatzki,Nouv. Ann. Math,2,,,1862,529,540,Early chinese treatment of quartic,1,0,

,29,0,0,0,0,0,Treutlein P.,,,Das Rechnen in 16. Jahrhundert,Abh. Gesch. Math.,1,,,1877,64,65,Early square root,1,0,

,19,0,0,0,0,0,Sédillot L.,,,Matériaux pour servir á l'histoire comparée des sciences mathématiques chez les Grecs et les Orientaux. 2 vols.,,,,Paris,1849,0,0,,1,0,

,19,29,0,0,0,0,Mikami Y.,,,The influence of Abaci on the Chinese and Japanese Mathematics,Jahresb. Deutsch. Math.-Verein..,20,,,1911,380,393,Roots, quadratics, and cubics by abacus,1,0,

,29,0,0,0,0,0,Lam L.Y.,,,On the existing fragments of Yang Hui's "Hsiang Chieh Suan Fa",Arch. Hist. Exact Sci.,6-1,,,1969,82,88,Chinese treatment of fourth root,1,0,

,19,0,0,0,0,0,Karpinski L.C.,,,The Algebra of Abu Kamil,Amer. Math. Monthly,21 (2),,,1914,37,0,Quadratics among the Arabs,1,0,

,19,25,0,0,0,0,Betti E.,,,Opere matematiche,,,Hoepli,Milano,1903,0,0,Considers solution by radicals, and cubics,1,0,

,19,0,0,0,0,0,Bortolotti E.,,,Storia della matematica elementare, in Enciclopedia delle Matematiche Elementari, ed L. Berzolari,,,Hoepli,Milano,1962,0,0,Includes history of low-degree polynomials,1,0,

,1,2,7,14,26,0,Beckett R.,Hurt J.,,Numerical Calculations and Algorithms,,,McGraw-Hill,New York,1967,0,0,Treats bisection, Newton, secant, Muller, Bairstow, error estimation,1,0,

,19,0,0,0,0,0,van Hée L.,,,Li Yeh, mathématicien chinois du III^e siècle,T'oung Pao Ser. 2,14,,,1913,537,568,Early quadratic,1,0,

,29,0,0,0,0,0,Bruins E.M.,,,Some Mathmatical Texts,Sumer,10,,,1954,55,61,Square and cube roots,1,0,

,19,0,0,0,0,0,Taha Baqir,,,Another important mathematical text from Tell Harmal,Sumer,6,,,1950,130,147,Ancient quadratics,1,0,

,29,0,0,0,0,0,Bruins E.M.,,,Revision of the mathematical texts from Tell Harmal,Sumer,9,,,1953,241,251,sqrt(2),1,0,

,1,2,7,14,15,0,Al-Khafaji A. W.,Tooley J.R.,,Numerical Methods in Engineering Practise,,,Holt, Rinehart & Winston,New York,1986,0,0,Treat bisection, Newton, reguli falsi, a second derivative method, and Bairstow,1,0,

,1,2,7,0,0,0,Atkinson K.E.,,,An Introduction to Numerical Analysis 2/E,,,Wiley,New York,1985,0,0,Treats bisection, Newton, secant,1,0,

,19,0,0,0,0,0,Rodet L.,,,L'Algèbre d'Al-Kharizmi,J. Asiatique Ser. 7,11,,,1878,38,0,early quadratic,1,0,

,19,0,0,0,0,0,Nasr S.H.,,,Science and Civilization in Islam,,,Harvard Univ. Press,,1968,158,0,brief quadratics,1,0,

,2,4,14,19,0,0,Salvadori M.G.,Baron M.L.,,Numerical Methods in Engineering 2/E,,,Prentice Hall,Englewood Cliffs NJ,1961,0,0,Treats Newton, Graeffe, Bairstow, quartic,1,0,

,1,2,3,7,17,19,Guggenheimer H.,,,BASIC Mathematical Programs for Engineers and Scientists,,,Petrocelli Books,West Hempstead NY,1987,0,0,Treats bisection, Newton, secant, Muller, simultaneous method, cubic,1,0,

,1,2,7,17,0,0,Hopkins T.,Philips C.,,Numerical Methods in Practise using the NAG Library,,,Addison-Wesley,Reading Mass,1988,0,0,Treats bisection, Newton, secant, evaluation,1,0,

,1,2,7,14,24,0,Hultquist P.F.,,,Numerical Methods for Engineers and Computer Scientists,,,Benjamin/ Cummings,Menlo Park, Cal,1988,0,0,Treats bisection, Newton, secant, acceleration, Bairstow,1,0,

,19,0,0,0,0,0,Gulibeau L.,,,The History of the Solution of the cubic equation,Nat. Math. Mag,5(4),,,1930,8,12,Title says it,1,0,

,1,2,7,14,19,0,Tuma J.J.,,,Handbook of Numerical Calculations in Engineering,,,McGraw-Hill,New York,1989,0,0,Treats bisection, Neton, secant, low-degree, Bairstow,1,0,

,1,2,7,0,0,0,Turner P.R.,,,Guide to Numerical Analysis,,,CRC Press,Boca Raton, Fla,1989,0,0,Treats bisection, Newton, secant,1,0,

,2,7,0,0,0,0,Wilkes M.V.,,,A Short Introduction to Numerical Analysis,,,CUP,New York,1966,0,0,Treats Newton, reguli falsi,1,0,

,25,0,0,0,0,0,Tannery J.,,,Manuscrits d'Évariste Galois,,,Gauthier-Villars,Paris,1908,0,0,,1,0,

,25,0,0,0,0,0,Tannery J.,,,Manuscrits et papiers inéditée de Galois,Bull. Sci. Math.,,,,1907,275,308,,1,0,

,19,0,0,0,0,0,Heiberg J.L.,,,Geschichte der Mathematik und Naturwissenschaften in Altertum,,,,Munchen,1925,0,0,Ancient quadratic,1,0,

,19,25,0,0,0,0,Bashmakova I.,Smirnova G.,,The Beginnings and Evolution of Algebra,,,Math. Assoc. Amer,,2000,0,0,History of low-degree, existence, solution by radicals,1,0,

,3,0,0,0,0,0,Wu X.,,,On zeros of a polynomial and vector solutions of associated polynomial systems from Vieta theorem.,Appl. Numer. Math.,44,,,2003,415,423,uses Broyden's method for the system. Claims better for multilpe zeros,1,0,

,3,0,0,0,0,0,Kjurkchiev N.,Iliev A.,,On the R-order of convergence of a family of methods for simultaneous extraction of part of all roots of algebraic polynomials,BIT,42,,,2002,879,885,Durand-Kerner method modified for a few roots.,1,0,

,2,19,29,0,0,0,Reynaud A.A.L.,,,Traité d'algèbre,,,,Paris,1821,0,0,Treats Newton, surds, quadratics,1,0,

,2,4,7,10,19,0,Mineur H.,,,Techniques de Calcul Numérique,,,Dunod,Paris,1966,0,0,Treats Newton, Graeffe, Sturm, secant, low-degree,1,0,

,19,0,0,0,0,0,Ruska J,,,Zur altesten arabischen Algebra und Rechenkunst,Sitz. Heidelberger Akad. Wiss.,8(2),,,1917,1,125,Arabic quadratics,1,0,

,10,25,0,0,0,0,de Comberousse C.,,,Cours de Mathématiques,,,Gauthier-Villars,Paris,1890,0,0,Treats existence, solution by radicals, Sturm, etc.,1,0,

,0,0,0,0,0,0,de Goeje,,,Annales quas scripsit.. Djarin al-Tabari,,,,,0,0,0,,1,0,

,25,0,0,0,0,0,De Peslouan C.L.,,,N.-H. Abel--sa vie et son oeuvre,,,Gauthier-Villars,Paris,1906,0,0,Touches on solution by radicals,1,0,

,2,4,10,19,25,0,Derwidué L.,,,Introduction á l'algèbre supérieure et au calcul numérique,,,Masson,Paris,1957,0,0,Treat Newton, Graeffe, Sturm etc, low-degree, existence,1,0,

,19,0,0,0,0,0,Story W.E.,,,Omar Khayyam as a mathematician,,,Rosemary Press,,1918,0,0,Very brief treatment of cubic,1,0,

,19,29,0,0,0,0,Juschkewitsch A.P.,Rosenfeld B.A.,,Die mathematik der Lander des Ostens im Mittelalter,,,,Berlin,1963,0,0,Treats quadratic, other low-degree equations, and surds,1,0,

,2,10,19,25,0,0,Cipolla M.,,,Analisi Algebrica,,,,,0,0,0,Treats Sturm etc, Newton, existence, low-degree,1,0,

,10,0,0,0,0,0,Yap C.K.,,,Fundamental Problems of Algorithmic Algebra,,,Oxford,,1999,0,0,,1,0,

,23,0,0,0,0,0,Ghersi I.,,,Matematica dilettevole e curiosa,,,Hoepli,Milano,1978,0,0,Section on mechanical devices,1,0,

,3,0,0,0,0,0,Illief L,Dochev,,Uber Newtonsche Iterationen,Wiss. Zeit. Tech. Hochsch. Dres.,12,,,1963,117,118,Original paper on simultaneous methods.,1,0,

,11,0,0,0,0,0,Routh E.J.,,,Stability of Motion ed. A.T.Fuller,,,Taylor & Francis,London,1975,0,0,,1,0,

,10,19,0,0,0,0,Mayer,Choquet C,,Traité élémentaire d'agèbre,,,,Paris,1832,0,0,Early statement of Sturm's Theorem. Also low-degree.,1,0,

,10,0,0,0,0,0,Porter M.B.,,,On the roots of functions connected to a linear recurrent relation of the second order,Ann. Math. Ser. 2,3,,,1901,55,70,Treats Sturm's Theorem,1,0,

,21,0,0,0,0,0,Driver K,Duren P,,Asymptotic zero distribution of hypergeometric polynomials,Numerical Algorithms,21,,,1999,147,156,,1,0,

,11,0,0,0,0,0,Bialas S,Garloff J,,Convex combinations of stable polynomials,J. Franklin Inst.,319,,,1985,373,377,,1,0,

,11,0,0,0,0,0,Peterson I.R.,,,A class of stability regions for which a Kharitonov type theorem holds,IEEE Trans. Automat. Control,34,,,1989,1111,1115,,1,0,

,11,0,0,0,0,0,Peterson I.R.,,,A new extension to Kharitonov's theorem,Proc. 26th IEEE Conf. Decision a Control,,,,1987,2070,2075,,1,0,

,11,0,0,0,0,0,Djaferis T.E.,Hollot C.V.,,The stability of a family of polynomials can be deduced from a finite number O(k³) of frequency checks,IEEE Trans. Automat. Control,34,,,1989,982,992,,1,0,

,11,0,0,0,0,0,Djaferis T.E.,Hollot C.V.,,Parameter partitioning via shaping conditions for the stability of families of polynomials,IEEE Trans. Automat. Control,34,,,1989,1205,1209,,1,0,

,11,0,0,0,0,0,Soh Y.C.,Foo Y.K.,,On the existence of strong Kharitonov theorems for interval polynomials,Proc. IEEE Conf Decision and Control,,,,1989,1882,1887,,1,0,

,11,0,0,0,0,0,Katbab A,Jury E.I.,,Robust Schur stability of a complex-coeffecient polynomial set with coefficients in a diamond,J. Franklin Inst.,327,,,1990,687,698,,1,0,

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,10,0,0,0,0,0,Acosta D.J.,,,Newton's Rule of Signs for Imaginary Roots,Amer. Math. Monthly,110,,,2003,694,706,If Q_i = a_i²-a_i+1a_i-1 (i=1,…,n-1); Q_n = a_n²; Q₀ = a₀², then number of variations in sign in Q_n,…,Q₀ is a lower bound for the number of complex roots.,1,0,

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,7,15,19,0,0,0,Pachner J,,,Handbook of numerical analysis applications,,,McGraw-Hill,New York,1984,0,0,Treats Secant, Laguerre, and low-degree,1,0,

,11,0,0,0,0,0,Soh C.B.,Berger C.S.,,Damping margins of polynomials with perturbed coefficients,IEEE Trans. Autom. Control,33,,,1988,509,511,Generalizes Kharitonov's theorem to sectors in complex plane,1,0,

,18,0,0,0,0,0,Diaz-Barrero, J.L.,,,Note on Bounds of the Zeros,Missouri J. Math. Sciences,14,,,2002,88,91,Bounds involve binomial coefficients and Fibonacci numbers,1,0,

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,11,0,0,0,0,0,Djaferis, T. J.,,,Shaping Conditions for the Robust Stability of Polynomials with Multilinear Parameter Uncertainty,Proc. 27th IEEE Conf. Dec. Contr.,,,,1988,526,531,,1,0,

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,21,0,0,0,0,0,Calogero F,Perelomov A.M.,,"Asymptotic density of zeros of Hermite polynomials of diverging order and related properties of certain singular integral operators",Lett. Nuovo Cimento,23,,,1978,650,652,,1,0,

,11,0,0,0,0,0,Bose N.K.,,,A system-theoretic approach to the stability of sets of polynomials, in "Linear algebra and its role in system theory" ed. R.A. Brualdi et al,Amer. Math. Soc.,,,Providence R.I.,1985,25,34,,1,0,

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,19,0,0,0,0,0,Matthiessen,,,"Goniometrische Auflösung der algebraischen Gleichungen der ersten vier Grade mittels der Formel für die Tangente des vielfachen Winkels",Arch. Math. Phys. Ser 3,2,,,1902,109,110,Trigonometric treatment of low degree polynomials,1,0,

,21,0,0,0,0,0,Goh W.M.Y.,Wimp J,,"On the asymptotics of the Tricomi-Carlitz polynomials and their zero distributions",SIAM J. Math. Anal.,25,,,1994,420,428,,1,0,

,21,0,0,0,0,0,Nevai P,Van Assche W,,"Remarks on the (C, -1) summability of the distribution of zeros of orthogonal polynomials",Proc. Amer. Math. Soc.,122,,,1994,759,767,,1,0,

,21,0,0,0,0,0,Kuijlaars A.B.J.,Serra Capizzano S.,,"Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients",J. Approx. Theory,113,,,2001,142,155,,1,0,

,21,0,0,0,0,0,Reimer M,,,The main-roots of the Euler-Frobenius polynomials,J. Approx. Theory,45,,,1985,358,363,Considers largest root less than or equal to -1.,1,0,

,7,0,0,0,0,0,Richard F.K.,,,An improved Pegasus method for root finding,BIT,13,,,1973,423,427,Variation on reguli falsi with efficiency 1.642, about same as Muller,1,0,

,2,15,0,0,0,0,Lang M,Frenzel B,,Polynomial root finding,IEEE Signal Proc. Lett.,1,,,1994,141,143,Combines Muller and Newton method. Better than Jenkins-Traub or eigenvalue methods,1,0,

,2,4,16,10,0,0,John F,,,Lectures on Advanced Numerical Analysis,,,Gordon and Breach,New York,1966,0,0,Treats Newton, Sturm, Bemoulli, Graeffe,1,0,

,11,0,0,0,0,0,Anderson B.D.O.,Jury E.I.,Mansour M,On robust Hurwitz polynomials,IEEE Trans. Automat. Control,AC-32,,,1987,909,913,For n= 3,4,5 the number of polynomials needed to check robust stability is 1,2,3. For n greater than or equal to 6 it is 4.,1,0,

,13,0,0,0,0,0,Herzberger J,,,"Bounds for the R-order of certain iterative numerical processes",BIT,26,,,1986,259,262,,1,0,

,13,0,0,0,0,0,Herzberger J,,,"On the R-order of some recurrences with applications to inclusion methods",Computing,36,,,1986,175,180,,1,0,

,13,0,0,0,0,0,Kjurckchiev N,,,"Note on the estimation of the order of convergence of classes of iterative processes",BIT,32,,,1992,525,528,Relates to R-order,1,0,

,2,15,0,0,0,0,Petkovic, M.,Herceg, D.,,On rediscovered iteration methods for solving equations,J. Comput. Appl. Math.,107,,,1999,275,284,Shows that a class of iterative methods presented by Gerlach is equivalent to other well-known classes derived earlier.,1,0,

,21,0,0,0,0,0,Gilewicz, J.,Leopold, E.,,Zeros of polynomials and recurrence relations with periodic coefficients.,J. Comput. Appl. Math.,107,,,1999,241,255,Zeros of a famaily of polynomials defined by 3-term recurrence relations with periodic coefficients are evaluated with the help of Chebyshev polynomials.,1,0,

,2,7,15,21,0,0,Herzberger, J.,,,Bounds for the positive roots of a class of polynomials with applications.,BIT,39,,,1999,366,372,Solving problems of effective rate of an annuity leads to new bounds for the positive root of p(t) ≡ tⁿ-aΣ_ν=1ⁿ t^n-ν. The result also applies to the rate of convergence of interpolatory root-finding methods.,1,0,

,19,0,0,0,0,0,Nicholson, P.,,,A Practical System of Algebra,,,,London,1831,0,0,Method similar to Horner's.,1,0,

,13,0,0,0,0,0,Nicholson, P.,,,Essay on Involution and Evolution,,,Davis & Dickson,London,1831,0,0,Treats low-degree polynomials, and gives and ad hoc method for higher degree.,1,0,

,20,0,0,0,0,0,Lidl, R.,,,Computational Problems in the Theory of Finite Fields,Appl. Alg. Eng. Comm. Comp.,2,,,1991,81,89,Surveys methods of factorizing polynomials over finite fields, among other things.,1,0,

,20,0,0,0,0,0,Lenstra, H.W.,,,Algorithms for finite fields, in "Number Theory and Cryptography", Ed. J.H. Loxton,,,Cambridge Univ. Press,,1990,76,85,Discusses algorihms for factoring polynomials into irreducible factors.,1,0,

,19,0,0,0,0,0,Odstrcil, J.,,,New method of root calculation for quadratic equations,Casopis Pest. Mat. Fys.,7,,,0,102,113,,1,0,

,13,0,0,0,0,0,Bellavitis, G.,,,Di trovare le radici reali delle equazioni algebraische.,Mem. Ist. Ven. Sci. Let. Arti,3,,,1846,109,267,,1,0,

,19,20,0,0,0,0,Bellavitis, G.,,,Saggio sull'algebre degli imaginarii.,Mem. Ist. Ven. Sci. Let. Arti,4,,,1852,243,344,,1,0,

,19,0,0,0,0,0,Pavelle, R.,Wang, P.S.,,Macsyma from F to G,J. Symb. Comput.,1,,,1985,69,100,Polynomials up to quartic and some higher can be solved symbolically.,1,0,

,25,0,0,0,0,0,Walecki,,,Démonstration d'un théorème fondamental de la théorie des équations algébriques.,C.R. Acad. Sci. Paris,96,,,1883,772,773,Proof of existence.,1,0,

,26,0,0,0,0,0,Wilkinson, J.,,,Modern error anlaysis,SIAM Rev.,13,,,1971,548,568,Less error in deflation if division done in order of increasing powers of x.Better still is a compromise between forward and backward division.,1,0,

,17,0,0,0,0,0,Reingold, E.M.,Srocks, A.I.,,Simple proofs of lower bounds for polynomial evaluation, in "Complexity of Computer Computations", Ed. R. Miller and J. Thatcher.,,,Plenum Press,New York,1972,21,30,An n'th degree polynomial can be evaluated in Floor(n/2)+2 multiplications and n adds/subs, if cost of preconditioning is not counted.,1,0,,p> ,17,0,0,0,0,0,Cormen, T.,Leiserson, C.,Rivest, R.,Introduction to Algorithms,,,MIT Press,,1990,0,0,Considers evaluation via the FFT.,1,0,

,20,0,0,0,0,0,Kaltofen, E.,Lobo, A.,,Factoring high-degree polynomials by the black box Berlekamp algorithm, in "Proc. Internat. Symp. On Symbolic and Algebraic Computation (ISSAC '94)" ed. J. Von Zur Gathen,,,ACM Press,New York,1994,90,98,Uses solution of structured linear systems over finite fields and matrix-vector multiplication.,1,0,

,17,0,0,0,0,0,Heintz, J.,,,On the computational complexity of polynomials, in "Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes", Ed. L. Huget and A. Poli,,,Springer-Verlag,New York,1989,269,300,For evaluation of d-degree polynomials, number of operations is at least Ceil(3d/2) (roughly). Gives examples of polynomials that are "hard to compute",1,0,

,20,29,0,0,0,0,Dickson, L.E.,,,History of the Theory of Numbers Vol. 1,,,Chelsea,New York,1952,215,215,Gives a method of solving x² = c(mod p) where p is a prime 4h+1 and some quadratic non-residue g of p is known.,1,0,

,15,0,0,0,0,0,Jovanovi&cacute, B.,,,A method for obtaining iterative formulas of higher order.,Mat. Vesnik,9,,,1972,365,369,Given an iterative method x_n+1 = φ(x_n) of order k, we derive another method of order at least k+1, I.e. x_n+1 =(x_n-φ(x_n))/(1-φ'(x_n)/k),1,0,

,2,15,29,0,0,0,Candela, V.,Marquina, A.,,Recurrence relations of rational cubic method II. The Chebyshev method.,Computing,45,,,1990,355,367,Compares Newton, Chebyshev and Halley methods for simple functions including n'th roots. The latter 2 methods are better.,1,0,

,26,0,0,0,0,0,Schätzle, R.,,,On the perturbation of the zeros of complex polynomials,IMA J. Numer. Anal.,20,,,2000,185,202,,1,0,

,1,2,7,24,0,0,Quarteroni, A.,Sacco, R.,Saleri, F.,Matematica Numerica,,,Springer-Verlag,New York,1998,0,0,Usual elementary treatment of Secant, Newton, Bisection, Muller, Aitken acceleration,1,0,

,2,0,0,0,0,0,Yang, Z.,,,Computing Equilibria and Fixed Points,,,Kluwer,Boston,1999,239,264,Considers Kuhn's algorithm, a kind of 2-dimensional bisection method,1,0,

,4,0,0,0,0,0,Mourrain, B.,Pan, V.Y.,,Lifting/Descending Processes for Polynomial Zeros,J. Complexity,16,,,2000,265,273,Uses Graeffe's method and Chebyshev-like lifting to factorize p(z) into F(z)G(z),1,0,

,1,0,0,0,0,0,Kavvadias, D.J.,Makri, F.S.,Vrahatis, M.N.,Locating and computing arbitrarily distributed zeros,SIAM J. Sci. Comput.,21,,,2000,954,969,Uses a generalized bisection method,1,0,

,2,0,0,0,0,0,Fouret, G.,,,Sur la Méthode d'Approximation de Newton,Nouv. Ann. Math,,,,1890,567,585,Gives a condition on f'(x) and f''(x) so that Newton's method converges,1,0,

,2,4,0,0,0,0,Gourdon, X.,,,Algorithmic Aspects of the Fundamental Theorem of Algebra,INRIA Report no. 1852,,,,1993,0,0,Combines Graeffe's and Newton's methods to factorize P into FG where F and G are about the same degree. Slower than Jenkins-Traub method but more robust on high degree polynomials.,1,0,

,29,0,0,0,0,0,Clark, W.E.,,,The Aryabhatiya of Aryabhata,,,Univ. Chicago Press,,1930,0,0,Gives a crude method for square and cube roots, dated about 500 A.D.,1,0,

,29,0,0,0,0,0,Kaye, G.R.,,,Indian Mathematics,,,,Calcutta,1915,0,0,Treats square and cube roots,1,0,

,19,0,0,0,0,0,Spearman, B.K.,Williams, K.S.,,Dihedral quintic polynomials and a theorem of Galois,Indian J. Pure Appl. Math.,30,,,1999,839,846,Given 2 roots, finds others as rational functions of them.,1,0,

,19,29,0,0,0,0,Gurjar, L.V.,,,Ancient Indian Mathematics and Vedha,,,,Poona,1947,0,0,Describes use of continued fractions for square root.,1,0,

,19,29,0,0,0,0,Bag, A.K.,,,Mathematics in Ancient and Medieval India,,,Chaukhambha Orientalia,,1979,0,0,Considers quadratics and square roots,1,0,

,20,0,0,0,0,0,Rosen, K.H.,,,Elementary Number Theory and its Applications,,,Addison-Wesley,Reading, Mass.,1984,0,0,Considers quadratic residues,1,0,

,10,0,0,0,0,0,Brunie, C.,Picart, P.S.,,A Fast Version of the Schur-Cohn Algorithm,J. Complexity,16,,,2000,54,69,Counts number of roots in unit disk of a polynomial of degree d. If bit size is σ, time complexity is of order d²σlog(dσ) loglog(dσ).log(d),1,0,

,20,0,0,0,0,0,Lange, T.,Winterhof, A.,,Factoring polynomials over arbitrary finite fields,Theoret. Comput. Sci.,234,,,2000,301,308,Factors most polynomials of degree n over F_q in order n^2+εlog²q operations,1,0,

,15,0,0,0,0,0,Kalantari, B.,Gerlach, J.,,Newton's method and generation of a determinantal family of iteration functions,J. Comput. Appl. Math.,116,,,2000,195,200,,1,0,

,27,0,0,0,0,0,Farahmand, K.,Hannigan, P.,,On the expected number of zero crossings of a random algebraic polynomial,Non-Lin Anal, Theory, Meths,Appls,30,,,1997,1219,1224,Number of zero crossings depends on ratio μ²/σ²,1,0,

,20,0,0,0,0,0,Tonelli, A.,,,Sulla risoluzione della congruenza x²≡c(mod p^λ),Atti R. Accad. Lincei, Rend. (Ser. 5),1,,,1892,116,120,,1,0,

,1,0,0,0,0,0,Favati, P. et al,,,An infinite precision bracketing algorithm with guaranteed convergence,Numerical Algorithms,20,,,1999,63,73,Convergence of the classical bisection method is not ensured when no information on the behaviour of the function is available. A modified bisection algorithm with guaranteed convergence is proposed and an upper bound to its compuational cost is given.,1,0,

,5,10,0,0,0,0,Brunetto, M.A.O.C.,Claudio, D.M.,Trevisan, V.,An Algebraic Algorithm to Isolate Complex Polynomial Zeros using Sturm Sequences,Comput. Math. Appl.,39(3),,,2000,95,105,Uses Sturm sequences and Argument Principle to enumerate zeros in a rectangle,1,0,

,31,0,0,0,0,0,Fergola, E.,,,Ricerce sulla risoluzione per Serie di Un'Equazione Qualunque,Ann. Mat. Pura Appl.,1,,,1858,0,0,,1,0,

,22,0,0,0,0,0,Alesina, A.,Galuzzi, M.,,Addendum to the Paper "A New proof of Vincent's Theorem",Enseign. Math. (Ser. 2),45,,,1999,379,380,Their proof is different from Ostrowski's,1,0,

,22,0,0,0,0,0,Ostrowski, A.M.,,,Note on Vincent's theorem,Ann. Math. Ser. 2,52,,,1950,702,707,Improves upon a result of Uspensky concerning a bound related to Vincent's method,1,0,

,18,0,0,0,0,0,Mignotte, M.,Cerlienco, L.,Piras, F.,Computing the measure of a polynomial,J. Symb. Comput.,4,,,1987,21,23,Finds bounds on roots and number outside unit circle,1,0,

,2,0,0,0,0,0,Peitgen, H.O.,Richter, P.H.,,The beauty of fractals,,,Springer-Verlag,Berlin,1986,0,0,Considers regions of convergence of Newton's method,1,0,

,19,0,0,0,0,0,Sarton, G.,,,Six Wings: Men of Science in the Renaissance,,,Indiana Univ. Press,Bloomington,1957,0,0,Good history of Cardan, etc.,1,0,

,19,0,0,0,0,0,Wightman, W.P.D.,,,Science and the Renaissance Vol. 1,,,Oliver & Boyd,Edinburgh,1962,0,0,Historical approach to low order equations,1,0,

,19,0,0,0,0,0,Bhaskara,,,Siddhanta Siromani,,,,,1150,0,0,,1,0,

,17,0,0,0,0,0,Rabin, M.O.,Winograd, S.,,Fast Evaluation of Polynomials by Rational Preparation,Comm. Pure Appl. Math.,25,,,1972,433,458,With pre-conditioning, can evaluate in 1/n + O(log n) multiplies and ~n adds.,1,0,

,17,0,0,0,0,0,Revah, L.,,,On the number of multiplications/ divisions evaluating a polynomial with auxiliary functions.,SIAM J. Comput.,4,,,1975,381,392,For n < 9, minimum number is ceil[(n+2)/2]. For n>=9, it is almost always ceil[(n+1)/2].,1,0,

,7,0,0,0,0,0,Opitz, G.,,,Zum Vergleich von iterationsverfahren zur Gleichungsauflösung,Z. Angew. Math. Mech. (T),41,,,1961,48,50,Uses divided difference interpolation over several previous iterations,1,0,

,7,0,0,0,0,0,Opitz, G.,,,Gleichungsauflösung mittels einer speziellen Interpolation,Z. Angew. Math. Mech.,38,,,1958,276,277,Uses divided difference interpolation over several previous iterations,1,0,

,16,0,0,0,0,0,Kjurkchiev, N.,Herzberger, J.,,On some bounds for polynomial roots obtained when determining the R-order of iterative processes.,Serdica,19,,,1993,53,58,Order of convergence is bounded below by the unique positive root of a certain polynomial. We show some new estimates for this root.,1,0,

,10,17,18,20,0,0,Mignotte, M.,Stefanescu, D.,,Polynomials, An Algorithmic Approach,,,Springer-Verlag,New York,1999,0,0,Considers resultants, bounds on roots, factorization in finite fields and integers,1,0,

,29,0,0,0,0,0,Datta, N.,,,The Bakhshali Mathematics,Bull. Calcutta Math. Soc.,21,,,1929,1,60,Gives ancient Indian formula for square root,1,0,

,10,12,0,0,0,0,Johnson, J.R.,,,Real Algebraic Number Computation using Interval Arithmetic, in "ISSAC 92",,,ACM Press,,1992,195,205,If a polynomial with real algebraic number coefficients is replaced with one whose coefficients are intervals containing the algebraic numbers, it may be possible to isolate the real roots of the exact polynomial.,1,0,

,10,20,0,0,0,0,Wang, P.S.,,,Parallel Univariate p-adic lifting on Shared-memory Multiprocessors, in "ISSAC 92",,,ACM Press,,1992,168,176,Important in gcd and factorization over the integers,1,0,

,10,20,0,0,0,0,Fortuna, E.,Gianni, P.,,Square-Free Decomposition in Finite Characteristic: An Application to Jordan Form Computation,SIGSAM,33(4),,,1999,14,32,,1,0,

,17,20,0,0,0,0,Lewis, R.H.,Wester, M.,,Comparison of Polynomial-Oriented Computer Algebra Systems,SIGSAM,33(4),,,1999,5,13,Considers exact symbolic evaluation.,1,0,

,26,0,0,0,0,0,Stetter, H.J.,,,The Nearest Polynomial with a Given Zero, and Similar Problems,SIGSAM,33(4),,,1999,2,4,,1,0,

,19,0,0,0,0,0,Labat, R.,,,La Mesopotamie,,,Presses Univ. France,,1957,0,0,Gives (in effect) formula for roots of quadratic,1,0,

,19,29,0,0,0,0,Gericke, H.,,,Geschichte des Zahlbegriffs,,,,Mannheim,1970,0,0,History of surds and quadratics, including geometric method.,1,0,

,5,0,0,0,0,0,Ioakimidis, N.I.,,,Quadrature methods for the determination of zeros of transcendental functions--a review, in "Numerical integration: recent developments, software and applications", Keast, P. (ed),,,Reidel,Dordrecht,1987,61,82,,1,0,

,10,0,0,0,0,0,Hribernig, V.,Stetter, H.J.,,Detection and validation of clusters of polynomial zeros,J. Symb. Comput.,24,,,1997,667,681,Combines symbolic and floating-point methods,1,0,

,19,0,0,0,0,0,Gandz, S.,,,Isoperimetric Problems and the Origin of the Quadratic Equation,Isis,32,,,1940,103,115,Covers history of quadratic up to Arabs,1,0,

,19,0,0,0,0,0,Archibald, R.C.,,,Babylonian Mathematics,Isis,26,,,1936,63,81,Covers quadratics,1,0,

,19,0,0,0,0,0,Archibald, R.C.,,,Babylonian Mathematics with Special Reference to Recent Discoveries,Math. Teacher,29,,,1936,209,219,Treats quadratic,1,0,

,1,2,7,19,26,0,Stummel, F.,Hainer, K.,,Praktische Mathematik,,,Teubner,Stuttgart,1982,0,0,Treats Bisection, Newton, Secant, low order, and errors.,1,0,

,17,0,0,0,0,0,Clenshaw, C.W.,,,A note on the summation of Chebyshev series,Math. Comp.,9,,,1955,118,120,Truncated Chebyshev series may be evaluated without using tables of Chebyshev polynomials,1,0,

,13,0,0,0,0,0,Julian, W.,Mines, R.,Richman, F.,Algebraic numbers, a constructive development,Pac. J. Math.,74,,,1978,91,102,Considers factorization over number fields,1,0,

,21,0,0,0,0,0,Curtz, P.,,,Probleme Soumis,Gazette des Mathematiciens,52,,,1992,44,44,Asks whether certain polynomials arising in the study of differential equations have any real roots,1,0,

,25,0,0,0,0,0,Dutordoir, H.,,,Toute équation algébrique a une racine; démonstration nouvelle,Mathesis,,,,1882,1,20,Proof of fundamental theorem (existence),1,0,

,29,0,0,0,0,0,Agarwal, R.C.,et al,,New scalar and vector elementary functions for the IBM System/370,IBM J. Res. Dev.,30(2),,,1986,126,144,Describes always correct SQRT function,1,0,

,29,0,0,0,0,0,Monuschi, P.,Mezzalama, M.,,Survey of square rooting algorithms,IEE Proc. (Pt. E),137,,,1990,31,40,Considers direct (digit-by-digit) methods as well as Newton's and its derivations,1,0,

,3,10,13,20,0,0,Diaz, A.,Kaltofen, E.,Pan, Y.,Algebraic algorithms, in "The Computer Science and Engineering Handbook", A.B. Tucker (Ed.),,,CRC Press,,1997,226,249,Brief survey of simultaneous and other methods, as well as factorization over finite fields,1,0,

,20,0,0,0,0,0,Niederreiter, H.,,,New deterministic factorization algorithms for polynomials over finite fields,Contemp. Math.,168,,,1994,251,268,The title says it,1,0,

,19,29,0,0,0,0,Flegg,et al,,Nicolas Chuquet, Renaissance Mathematician,,,Reidel,,1985,112,0,Early treatment of square root and quadratic,1,0,

,13,0,0,0,0,0,Fitch, J.,,,Solving Algebraic Problems with REDUCE,J. Symb. Comput.,1,,,1985,211,227,Treats factorization of simple polynomials by symbolic methods,1,0,

,10,13,0,0,0,0,Loos, R.,,,Computing in Algebraic Extensions, in "Computer Algebra-Symbolic and Algebraic Computation", Ed. B. Buchberger et al,,,Springer-Verlag,,1982,173,188,,1,0,

,13,0,0,0,0,0,Van Hulzen, J.A.,Calmet, J.,,Computer Algebra Systems, in "Computer Algebra-Symbolic and Algebraic computation", Ed. B. Buchberger et al,,,Springer-Verlag,,1982,221,243,Brief treatment of symbolic root-finding,1,0,

,19,29,0,0,0,0,Berggren, J.L.,,,Episodes in the Mathematics of Medieval Islam,,,Springer-Verlag,New York,1986,0,0,Treats surds and quadratics among the Arabs,1,0,

,19,29,0,0,0,0,Bose, D.M. et al (eds),,,A Concise History of Science in India,,,Indian Nat. Acad. Sci.,New Delhi,1971,0,0,Treats surds, quadratic and cubic among the early Indians,1,0,

,19,29,0,0,0,0,Eells, W.C.,,,Greek Methods of Solving Quadratic Equations,Amer. Math. Monthly,18,,,1911,3,14,Treats square roots, including Heron's method, and geometric solution of quadratic.,1,0,

,13,19,29,0,0,0,Li, Y.,Shiran, D.,,Chinese Mathematics: A Concise History, Trans. J. Crossley and A. Lun,,,Clarendon Press,Oxford,1987,0,0,Treats surds, quadratics and higher degree equations among the Chinese,1,0,

,29,0,0,0,0,0,Singh, A.N.,,,On the Indian Method of Root Extraction,Bull. Calcutta Math. Soc,18,,,1927,123,140,Treats surds among the Indians,1,0,

,22,0,0,0,0,0,Alesina, A.,Galuzzi, M.,,A New Proof of Vicent's Theorem,Enseign. Math.,44,,,1998,219,256,Vincent's theorem uses continued fractions to separate roots. Proof given,1,0,

,10,0,0,0,0,0,Bartolozzi, M.,Franci, R.,,La regola dei segni dall'enunciato di R. Descartes (1637) alla dimostrazione di Gauss (1828),Arch. Hist. Exact Science,45,,,1993,335,374,Treats Descartes' rule of signs and proof by Gauss,1,0,

,22,0,0,0,0,0,Bombieri, E.,Van der Poorten, A.J.,,Continued fractions of algebraic numbers, in "Computational Algebra and Number Theory",,,Kluwer,Dordrecht,1995,137,152,Treats Vincent's method (continued fractions),1,0,

,2,10,19,29,0,0,Bourdon, L.P.M.,,,Élémens d'Algèbre,,,Bachelier,Paris,1891,0,0,Treats n'th roots, Newton and Sturm's methods, quadratic and cubic,1,0,

,22,0,0,0,0,0,Cantor, D.G.,Galyean, P.H.,Zimmer, H.G.,A continued fraction algorithm for real algebraic numbers,Math. Comp.,26,,,1972,785,791,Related to Vincent's theorem (continued fractions).,1,0,

,19,0,0,0,0,0,Smith, D.E.,Latham, M.L.,,The Geometry of Rene Descartes,,,Open Court Publ. Co.,La Salle, Ill.,1925,0,0,Gives geometrical solution of quadratic, cubic, and quartic.,1,0,

,29,0,0,0,0,0,Hart, J.F.,et al,,Computer Approximations,,,Wiley,New York,1968,0,0,gives good treatment of square and cube roots by Newton's method,1,0,

,19,0,0,0,0,0,Winter H.J.J.,,,Eastern Science,,,,London,1952,0,0,Treats quadratic among Indians and Arabs.,1,0,

,10,25,0,0,0,0,Young, J.W.A.,,,Monographs on Modern Mathematics,,,Longmans,,1955,0,0,Brief description of Existence and Sturm's Theorems,1,0,

,19,0,0,0,0,0,Ball, W.W. R.,,,A Short Account of the History of Mathematics,,,Macmillan,,0,0,0,History including quadratic and cubic.,1,0,

,10,0,0,0,0,0,Roy, M.-F.,Szpirglas, A.,,Complexity of computation of real algebraic numbers,J. Symb. Comput.,10,,,1990,39,51,Generalized Sturm sequence,1,0,

,2,26,0,0,0,0,Rump, S.M.,,,Algebraic computation, numerical computation and verified inclusion, in "Trends in Computer Algebra", Ed. R. Jansen,,,Springer-Verlag,Berlin,1988,177,197,Gives an example where computer gives wrong result with Newton's method.,1,0,

,29,0,0,0,0,0,Hay, C. (Ed.),,,Mathematics from Manuscript to Print:1300-1600.,,,Clarendon Press,Oxford,1988,0,0,Treats surds.,1,0,

,25,0,0,0,0,0,Taton, R.,,,Evariste Galois and his Contemporaries,Bull. London Math. Soc.,15,,,1983,107,118,Treats question of whether solution by radicals is possible,1,0,

,19,0,0,0,0,0,Boas, M.,,,The Scientific Renaissance,,,Harper,New York,1962,0,0,Brief history of cubic without equations.,1,0,

,3,0,0,0,0,0,Semerdzhiev, Kh.,,,Iterative Methods for Simultaneously Finding All Roots of Generalized Polynomial Equations.,Math. Balkanica (New series),8,,,1994,311,335,Method for finding multiplicities of zeros and simultaneous zero-finding.,1,0,

,2,0,0,0,0,0,Saupe, D.,,,Discrete versus continuous Newton's Method:: A case study,Acta Applic. Math.,13,,,1988,59,80,Damped Newton converges for a small damping factor,1,0,

,28,0,0,0,0,0,Borcea, I.,,,The Sendov conjecture for polynomials with at most seven zeros.,Analysis,16,,,1996,137,159,Relation between zeros of a polynomial and those of its derivative.,1,0,

,19,0,0,0,0,0,Nordgaard, M.A.,,,Sidelights on the Cardan-Tartaglia Controversy,National Math. Magazine,12,,,1937,327,346,Good history of solution of cubic.,1,0,

,19,0,0,0,0,0,Stoll,,,Zur Losung der kubischen Gleichungen,,,,Bensheim,1876,0,0,Treats trigonometric solution of cubic,1,0,

,10,0,0,0,0,0,Borodin, A.,von zur Gathen, J.,Hopcroft, J.,Fast Parallel Matrix and gcd Computations, Tech. Rep. 156/82,,,COSC Dept, Univ. Toronto,,1982,0,0,Finds gcd of n'th degree polynomial in O(log² n) time and polynomial number of processors.,1,0,

,13,0,0,0,0,0,Wolfram, S.,,,Mathematica: A System for Doing Mathematics by Computer, 2/E,,,Addison-Wesley,Redwood City, Calif.,1991,0,0,Treats Symbolic methods,1,0,

,20,0,0,0,0,0,von zur Gathen, J.,Gerhardt, J.,,Arithmetic and Factorization over F₂, in "Proc. ISSAC '96", ed. Y.N. Lakshman,,,ACM,,1996,1,9,,1,0,

,20,0,0,0,0,0,von zur Gathen, J.,Hartlieb, S.,,Factoring Modular Polynomials, in "Proc. ISSAC '96", ed. Y.N. Lakshman,,,ACM,,1996,10,17,,1,0,

,1,7,13,0,0,0,Collins, G.E.,Krandick, W.,,A Tangent-Secant Method for Polynomial Complex Root Calculation, in "Proc. ISSAC '96", ed. Y.N. Lakshman,,,ACM,,1996,137,141,Gives a hybrid symbolic-numeric method, using winding numbers and rectangle bisection.,1,0,

,29,0,0,0,0,0,Ahrendt, T.,,,Fast High-Precision Computation of Complex Square Roots, in "Proc. ISSAC '96", ed. Y.N. Lakshman,,,ACM,,1996,142,149,One algorithm uses "pencil-and-paper" method, is of order n², and useful for about 100 digits. The other uses a variation of Newton's method, is of order (nlogn loglog n), and is useful for about 1000 digits.,1,0,

,28,0,0,0,0,0,Brown, J.E.,,,A proof of the Sendov Conjecture for polynomials of degree seven.,Complex Variables Theory Appl.,33,,,1997,75,95,Relation between zeros of a polynomial and those of its derivative.,1,0,

,28,0,0,0,0,0,Katsoprinakis, E.S.,,,Errarum To "on the Sendov-Illyeff Conjecture",Bull. London Math. Soc.,28,,,1996,605,612,Relation between zeros of a polynomial and those of its derivative.,1,0,

,2,15,0,0,0,0,Flanders, H.,,,Scientific Pascal 2/E,,,Springer-Verlag,New York,1996,0,0,Programs in Pascal for Newton's and Halley methods,1,0,

,19,0,0,0,0,0,Smith, D.E.,,,Mathematics,,,Cooper Square Publ.,New York,1963,0,0,Gives Heron's solution of a quadratic,1,0,

,20,0,0,0,0,0,Gouvea, F.Q.,,,p-adic Numbers: An Introduction,,,Springer-Verlag,New York,1991,0,0,Deals with congruences,1,0,

,20,0,0,0,0,0,Koblitz, N.,,,p-adic Numbers, p-adic Analysis, and Zeta-Functions,,,Springer-Verlag,New York,1977,0,0,Deals with congruences,1,0,

,10,17,0,0,0,0,Bürgisser, P.,Clausen, M.,Shokrollahi, M.A.,Algebraic Complexity Theory,,,Springer-Verlag,New York,1997,0,0,Sections on gcd and evaluation,1,0,

,2,14,15,17,26,0,Fox, L.,Mayers, D.F.,,Computing Methods for Scientists and Engineers,,,Clarendon Press,Oxford,1968,0,0,Treats evaluation including errors, Newton and Laguerre briefly, conditioning, and errors in computed zeros,1,0,

,16,0,0,0,0,0,Schmidt, J.W.,,,Beitrage zur Convergenzordnung bei Iterationsverfahren,Nova Acta Leopoldina (New Ser.),61,,,1989,97,105,,1,0,

,20,0,0,0,0,0,Bartholdi, L.,,,Lamps, Factorizations, and Finite Fields,Amer. Math. Monthly,107,,,2000,429,436,Considers factorization of Xⁿ+X+1 over field F₂,1,0,

,20,0,0,0,0,0,Flajolet, P.,Gourdon, X.,Panario, D.,Random polynomials and polynomial factorization in "Proc. ICALP '96" eds F. Meyer et al,,,Springer-Verlag,New York,1996,232,243,,1,0,

,29,0,0,0,0,0,Lickteig, T.,Werther, K.,,How can a complex square root be computed in an optimal way?,Comput. Complexity,5,,,1995,222,236,Title says it (square roots),1,0,

,23,29,0,0,0,0,Fenton, P.C.,,,Eratosthenes cube root mechanism,Math. Gaz.,84,,,2000,287,289,Describes a mechanical method for finding cube (and square) roots.,1,0,

,29,0,0,0,0,0,Desbrow, D.,,,Approximation to square roots…,Math. Gaz.,84,,,2000,282,287,Gives high order iteration for square root,1,0,

,29,0,0,0,0,0,Ercegovac, M.D. et al,,,Reciprocation, Square Root,…,IEEE Trans. Comput.,49,,,2000,628,637,Method based on argument reduction and series expansion allows high precision square root etc.,1,0,

,1,13,0,0,0,0,Wang, Z.,,,On the efficiency of Kuhn's root-finding algorithm,Kexue Tongbao,27,,,1982,1023,1023,,1,0,

,29,0,0,0,0,0,Ramanujacharia, N,Kaye, G.R.,,The Trisatika of Sridharacarya,Bibl. Math. (Ser. 3),13,,,1912,203,217,Gives ancient indian verbal rule for square root,1,0,

,27,0,0,0,0,0,Erdös, P.,Offord, A.C.,,On the number of real roots of a random algebraic equation.,Proc. London Math. Soc. (Ser. 3),6,,,1956,139,160,

$Number of real roots of polynomial with coefficients \pm 1 is usually ~ \frac{2}{π} log n$

,1,0,

,20,0,0,0,0,0,Loos, R.,,,Computing rational zeros of integral polynomials by p-adic expansion,SIAM J. Comput.,12,,,1983,286,293,

$Method has maximum time of order n^{3} {L (d)}^{2} where d = Σ | a_{i} |$

,1,0,

,10,0,0,0,0,0,Reischert, D.,,,Asymptotically fast computation of subresultants, in ISSAC '97",,,Assoc. Comput. Mach.,New York,1997,233,240,,1,0,

,2,25,0,0,0,0,Heuser, H,,,Lehrbuch der Analysis I,,,Teubner,Stuttgart,1994,0,0,Considers existence and Newton's method,1,0,

,20,25,0,0,0,0,Spearman, B.K.,,,Quadratic subfields of the splitting field of a dihedral quintic trinomial x⁵+ax+b,New Zealand J. Math.,26,,,1997,293,299,,1,0,

,25,0,0,0,0,0,Spearman, B.K.,Williams, K.S.,,Characterization of solvable quintics x⁵+ax+b,Amer. Math. Monthly,101,,,1994,986,992,Characterizes irreducible quintics which are solvable by radicals,1,0,

,10,11,0,0,0,0,Lickteig, T.,Roy, M.F.,,Cauchy index computation,Calcolo,33,,,1996,337,351,Computes Cauchy Index of Q/P in time of order d log²(d+1) where d = degree of P.,1,0,

s2aj13,1,2,,,,,Alefeld G.E.,Potra F.A.,Shi Y.,Algorithm 748: Enclosing Zeros of Continuous Functions,ACM Trans. Math. Software,21,,,1995,327,344,,1,,

s2aj14,2,12,,,,,Alefeld G.E.,Potra F.A.,Völker W.,Modifications of the Interval Newton Method with Improved Asymptotic Efficiency,BIT,38,,,1998,619,635,,1,,

s2aj15,19,,,,,,Alexandre R.,,,Note sur le moyen de ramener une équation quelconque du quatrième degré à une équation réciproque du même degré,Nouv. Ann. Math.,25,,,1866,477,478,,1,,

,10,0,0,0,0,0,Pragacz P,,,A note on elimination theory,Akad. Wet. Amster. Proc. Math. Sci.,90,,,1987,215,221,Generalizes resultant,1,0,

,19,0,0,0,0,0,Hoyrup J.,,,Al-Khwarizmi, Ibn Turk, and the Liber Mensurationum: on the origins of Islamic algebra,Erdem,5,,,1986,445,484,Arabic quadratics,1,0,

,29,0,0,0,0,0,Chemla K.,,,Similarities between Chinese and Arabic mathematical writings: (1) Root extraction,Arabic Sciences and Philosophy,4,,,1994,207,266,Chinese and Arabic root extraction,1,0,

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,10,0,0,0,0,0,Sasaki T.,Noda M.-T.,,Approximate square-free decomposition and root-finding of ill-conditioned algebraic equations,J. Inf. Process.,12,,,1989,159,168,Uses generalized Euclidean algorithm,1,0,

,10,17,0,0,0,0,von zur Gathen J.,Gerhard J.,,Modern Computer Algebra 2/E,,,Cambridge University Pr.,,1999,0,0,Good treatment of resultants, GCD, evaluation.,1,0,

,10,0,0,0,0,0,Brodie S.E.,,,Descartes' Rule of Signs, found at: http://www.cut-the-knot.com/fta/ROS2.shtml,,,,,0,0,0,Prove's Descartes' rule.,1,0,

,19,0,0,0,0,0,Descartes R.,,,The Geometry of René Descartes with a Facsimile of the First Edition. Trans. D.E. Smith and M.L. Latham,,,Dover,New York,1954,0,0,Geometric treatment of cubic and quartic,1,0,

,25,0,0,0,0,0,Kowalsky H.-J.,,,Zum Fundamentalsatz der Algebra,Braunschw. Wiss. Ges. Abh.,35,,,1983,111,120,Treats existence, apparently using matrices and determinants.,1,0,

,10,0,0,0,0,0,Winkler J.R.,,,The transformation of the companion matrix resultant between the power and Bernstein polynomial bases.,Appl. Numer. Math.,48,,,2004,113,126,Resultant should be constructed directly in Berstein base.,1,0,

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,20,0,0,0,0,0,Dickson L.E.,,,Linear Groups with an Exposition of the Galois Field Theory,,,Dover Publications Inc.,New York,0,0,0,Roots in finite fields.,1,0,

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,11,0,0,0,0,0,Steffen P,,,An algorithm for testing stability of discrete systems.,IEEE Trans. Acoust. Speech, Signal Processing,ASSP-25,,,1977,454,456,Uses continued fractions.,1,0,

,11,0,0,0,0,0,Ismail M,,,A simplified algorithm for testing stability of discrete systems via bilinear continued fractions.,IEEE Trans. Circuits Syst.,CAS-33,,,1986,544,547,,1,0,

,11,0,0,0,0,0,Gnanasekaran R,,,A note on the new 1-D and 2-D stability theorems for discrete systems.,IEEE Trans. Acoust. Speech, Signal Processing,ASSP-29,,,1981,1211,1212,,1,0,

,25,0,0,0,0,0,Pesic P,,,Abel's Proof,,,MIT Press,,2003,0,0,Popular treatment of non-solubility by radicals for degree > 4.,1,0,

,11,0,0,0,0,0,Ackermann J,Barmish B.R.,,Robust Shur stability of a polytope of polynomials,IEEE Trans. Automat. Control,AC-33 no. 10,,,1988,984,986,Condition for polytope of polynomials to have all its zeros in unit circle.,1,0,

,21,0,0,0,0,0,Barrios D,Lopez G,Torrano E,Location of zeros and asymptotics of polynomials satisfying three-term recurrence relations with complex coefficients.,Russian Acad. Sci. Sb. Math.,80,,,1995,309,333,,1,0,

,21,0,0,0,0,0,Garcia P,Marcellan F,,On zeros of regular orthogonal polynomials on the unit circle.,Ann. Polon. Math.,58,,,1993,287,298,,1,0,

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,21,0,0,0,0,0,Saff E.B.,Totik V.,,What parts of a measure support attracts zeros of the corresponding orthogonal polynomials?,Proc. Amer. Math. Soc.,114,,,1992,185,190,,1,0,

,21,0,0,0,0,0,Siafarikas P.D.,,,Inequalities for the zeros of the associated ultraspherical polynomials.,Math. Ineq. Appl.,2,,,1999,233,241,,1,0,

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,25,0,0,0,0,0,Horowitz L,,,A proof of the "fundamental theorem of algebra" by means of Galois theory and 2-Sylow groups.,Nieuw Arch. Wisk. Ser. 3,14,,,1996,95,96,Brief proof of existence.,1,0,

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,10,0,0,0,0,0,Mourges H,,,Note sur le théorème de Sturm,Nouv. Ann. Math.,9,,,1850,278,279,,1,0,

,18,0,0,0,0,0,Biernacki M,,,Sur l' équation du troisième degré.,Mathematica,8,,,1934,196,200,Considers bounds on roots of a cubic.,1,0,

,19,0,0,0,0,0,Natucci A.,,,Storia della teoria delle equazioni. I. Dall'antichita all'inizio del secolo XVI⁰ (Capitolo I),Period. Mat.,41,,,1963,1,16,Brief quadratic.,1,0,

,11,0,0,0,0,0,Chen C.F.,Tsay Y.T.,,A new formula for the discrete-time system stability test.,Proc. IEEE,65,,,1977,1200,1202,,1,0,

,28,0,0,0,0,0,Erdos P,Niven I,,On the roots of a polynomial and its derivative.,Bull. Amer. Math. Soc.,54,,,1948,184,190,,1,0,

,20,0,0,0,0,0,Niederreiter H,,,Factoring polynomials over finite fields using differential equations and normal bases.,Math. Comp.,,,,1994,819,830,Better than Berlekamp.,1,0,

,20,0,0,0,0,0,Presic M.D.,,,A method for solving equations in finite fields.,Mat. Vesnik.,,,,1970,507,509,,1,0,

,20,0,0,0,0,0,Neiderreiter H (ed.),Mullen G.L. (ed.),Shiue P. J.-S. (ed.),Finite Fields: Theory, Applications, and Algorithms.,,,American Mathematical Soc,Brookline, MA,1994,0,0,Several articles on factorization over finite fields.,1,0,

,19,0,0,0,0,0,Berriman A.E.,,,The Babylonian quadratic equation.,Math. Gaz.,40,,,1956,185,192,,1,0,

,19,0,0,0,0,0,Jones P.S.,,,Recent discoveries in Babylonian mathematics III: trapeziods and quadratics.,Mathematics Teacher,50,,,1959,570,571,Ancient quadratics.,1,0,

,29,0,0,0,0,0,Jones P.S.,,,The square root of two in Babylonia and America.,Mathematics Teacher,42,,,1949,307,310,Early Surd.,1,0,

,19,0,0,0,0,0,Boyer C.B.,,,Early graphical solutions of polynomial equations.,Scripta,11,,,0,5,19,Used conic sections mostly for low-order.,1,0,

,25,0,0,0,0,0,Weber, H.,,,Die allgemeinen Grundlagen der Galois schen Gleichungs theorie,Math. Ann.,43,,,1893,521,549,Deals with Galcis theory of Equations,1,0,

,21,0,0,0,0,0,Assche, W. V.,,,"Zero distribution of orthogonal polynomials with asymptotically periodic varying recurrence coefficients" in "self-similar systems" ed. V.B. Prizzhiev,,,,Dubna,1999,392,402,,1,0,

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,3,0,0,0,0,0,Petkovic M.S.,Sakurai T.,Rancic L.,Family of Simultaneous methods of Hansen Patrick's type,Appl. Numer. Math,50,,,2004,489,510,Derives a new family of methods of order 4 in parallel mode, or > 4 in Gauss-Seidel-like mode. Includes multiple zeros.,1,0,

,3,12,0,0,0,0,Zhu L.,,,On the convergent condition of Newton-like method in parallel circular iteration for simultaneously finding all multiple zeros of a polynomial,Appl. Math. Comput.,152,,,2004,837,846,Disk version of Ehrlich-Aberth method for multiple roots.,1,0,

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,7,0,0,0,0,0,Glushkov S.,,,On Approximation Methods of Leonardo Fibonacci,Hist. Math.,3,,,1976,291,296,Solves a cubic by reguli false,1,0,

,3,0,0,0,0,0,Zhao, F.,Wang, D.,,The theory of Smale's point estimation and the convergence of Durand-Kerner program,Math. Numer. Sinica,15,,,1993,196,206,Title says it.,1,0,

,19,29,0,0,0,0,Rashed R.,,,Résolution des équations numériques et algèbre: Sharaf al-Din al-Tusi, Viète,Archive for History of Exact Sciences,12,,,1974,244,290,Deals with square root, cube root, low-degree,1,0,

,25,0,0,0,0,0,Ruffini, P.,,,Riflessoni intorno alle soluzioni della equazion algebraiche generale,Opere,2,,,1953,155,268,Treats solution by radicals,1,0,

,25,0,0,0,0,0,Abel, N.H.,,,Oeuvres Completes de N.H. Abel, Mathematicien. C. Grondahl, Christianian,,,Johnson Reprint Co.,New York and London,1965,0,0,Solution by radicals (or not),1,0,

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,19,0,0,0,0,0,Garver R.,,,Quartic Equations with Certain Groups,Annals of Math.,30,,,1928,47,51,,1,0,

,2,0,0,0,0,0,Gilbert, W. J.,,,The Complex Dynamics of Newton's Method for Multiple Roots,Comput. & Graphics,18,,,1994,227,229,Treats basins of attraction for Newton's method,1,0,

,2,0,0,0,0,0,Deuflhard, P.,,,Newton methods for non-linear problems,,,Springer,,2004,0,0,Good history of Newton's method for scalar equation,1,0,

,19,0,0,0,0,0,Jerrard, G.B.,,,Note on some objections of Mr Cayley & Mr Cockle…,Phil Mag,24,,,1862,193,195,Refers to quintics.,1,0,

,19,0,0,0,0,0,Hugues B.B.,,,Gerard of Cremona's translation of the al-Khwarizmi's 'Al-Jabr: A critical edition',Mediaeval Studies,48,,,1986,211,263,Early quadratics.,1,0,

,19,0,0,0,0,0,Hugues B.B.,,,Robert of Chester's translation of al-Khwarizmi's al-Jabr,,,Beothius XIV,Stuttgart,1989,0,0,Arabic quadratics,1,0,

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,10,0,0,0,0,0,Winkler, J.R.,,,Computational experiments with resultants for scaled Bernstein polynomials, in: T. Lyche, L.L. Schumaker (Eds.), Mathematical Methods for Curves and Surfaces: Oslo 2000,,,Vanderbilt Univ. Press,USA,2001,535,544,,1,0,

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,19,29,0,0,0,0,Giusti E.,,,Algebra and geometry in Bombelli and Viète,Boll. Storia Sci. Mat.,12-2,,,1992,303,328,Geometric solution of square and cube roots and quadratic.,1,0,

,29,0,0,0,0,0,Rivolo M.T.,Simi A.,,The computation of square and cube roots in Italy from Fibonacci to Bombelli (Italian),Arch. Hist. Exact Sci.,52-2,,,1998,161,193,No note,1,0,

,29,0,0,0,0,0,Martzloff J.-C.,,,Recherches sur l'oeuvre mathématique de Mei Wending (1633-1721),,,Inst. H. Etudes Chin.,,1981,0,0,Treats n'th roots,1,0,

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,10,0,0,0,0,0,Hong H.,,,Subresultants under composition.,J. Symb. Comput.,23(4),,,1997,355,365,Subresultants almost commute under composition.,1,0,

,2,0,0,0,0,0,Przytycki F.,,,"Remarks on the simple connectedness of basins of sinks for iterations of rational maps" in Dynamical Systems and Ergodic Theory, ed. K. Krzyzewski,,,Polish Scientific Pubs.,Warszawa,1989,229,235,Treats convergence of Newton's method.,1,0,

,17,0,0,0,0,0,Barrio R.,Sabadell F.J.,,Parallel evaluation of Chebyshev and trigonometric series,Computers Math. Applic.,38 (11/12),,,1999,99,106,No note.,1,0,

,17,0,0,0,0,0,Barrio R.,Sabadell F.J.,,A parallel algorithm to evaluate Chebyshev series on a message-passing environment.,SIAM J. Sci. Comp.,20,,,1998,964,969,No note.,1,0,

,17,0,0,0,0,0,Barrio R.,,,Stability of parallel algorithms to evaulate Chebyshev series.,Computers Math. Applic.,41 (10/11),,,2001,1365,1377,No note.,1,0,

,29,0,0,0,0,0,Speziali P.,,,"Luca Pacioli et son ouevre" in Sciences de la Renaissance: VIII Congrès International de Tour,,,,Paris,1973,93,106,Early treatment of square root.,1,0,

,19,0,0,0,0,0,Speziali P.,,,L' école algébriste italienne du XVI siècle et la résolution des equations des 3 et 4 degrés.in Sciences de la Renaissance: VIII Congrès International de Tour,,,,Paris,1973,107,120,History of cubic and quartic.,1,0,

,19,0,0,0,0,0,Gliozzi M.,,,Cardano, Girolamo. In Dictionary of Scientific Biography Vol 3,,,,,0,64,67,Solution of cubic.,1,0,

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,21,0,0,0,0,0,Elbert A.,Laforgia A.,,Upper bounds for the zeros of ultraspherical polynomials.,J. Approx. Theory,61,,,1990,88,97,No note.,1,0,

,21,0,0,0,0,0,Elbert A.,Laforgia A.,Rodono L.G.,On the zeros of Jacobi polynomials,Acta. Math. Hung.,64,,,1994,351,359,No note.,1,0,

,21,0,0,0,0,0,Elbert A.,Siafarikas P.D.,,Monotonicity properties of the zeros of ultraspherical polynomials.,J. Approx. Theory,97,,,1999,31,39,No note.,1,0,

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,2,0,0,0,0,0,Homeier H.H.H.,,,On Newton-type methods with cubic convergence.,J. Comput. Appl. Math.,176,,,2005,425,432,Uses 3 function evaluations.,1,0,

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,19,0,0,0,0,0,Cardano G.,,,Ars Magna,,,Dover,New York,1993,0,0,Solution of cubic.,1,0,

,19,0,0,0,0,0,Garver R.,,,A rational normal form for certain quartics.,Bull. Amer. Math. Soc.,34,,,1928,73,74,They can be reduced to quadratics.,1,0,

,19,20,0,0,0,0,Bucht G.,,,Über einige algebraische Körper achten Grades.,Ark. Mat. Astr. Fys.,6 (No. 30),,,1910,,0,Seems to treat quartic.,1,0,

,3,0,0,0,0,0,Petkovic M.S.,Stefanovic L.V.,Marjanovic Z.M.,On the R-order of some accelerated methods for the simultaneous finding polynomial zeros.,Computing,49,,,1993,349,361,Methods of order 4 through 7 for multiple roots.,1,0,

,18,0,0,0,0,0,Abels A.,Herzberger J.,,"A Unified Approach for Bounding the Positive Root of Certain Classes of Polynomials with Applications" in Topics in Numerical Analysis Ed. G. Alefeld.,,,Springer,Wien,2001,1,8,Applied to rates of convergence.,1,0,

,3,0,0,0,0,0,Petkovic M.S.,Petkovic L.,Zivkovic D.,"Laguerre-like Methods for the Simultaneous Approximation of Polynomial Zeros" in Topics in Numerical Analysis Ed. G. Alefeld.,,,Springer,Wien,2001,189,201,Orders 5 and 6 or higher.,1,0,

,10,0,0,0,0,0,Akritas A.G.,Akritas E.K.,Malaschonok G.I.,Matrix computation of subresultant polynomial remainder sequences in integral domains.,Reliable Computing,1,,,1995,375,381,No note.,1,0,

,10,0,0,0,0,0,Recio T.,Gonzalez-Vega L.,Lombardi H. and Roy M.-F.,Spécialisation de la suite de Sturm et sous-résultants.,RAIRO Inform. Theor. Applic.,24,,,1990,561,588,Generalizes Sturm sequences and sub-resultants, hence counts number of real roots.,1,0,

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,20,0,0,0,0,0,Kronecker,,,Grundzüge einer arithmetischen Theorie der algebraischen Grössen,,,,Berlin,1882,0,0,,1,0,

,19,0,0,0,0,0,Hofmann J.E.,,,Bombelli's Algebra. Eine genialische Einzelleistung und ihre Einwirkung auf Leibniz,Stud. Leibnitiana,4 (3-4),,,1972,196,252,Low-degree,1,0,

,29,0,0,0,0,0,Hofmann J.E.,,,Erklärungsversuche für Archimedes Berechnung von $\sqrt{3}$ ,Arch. Gesch. Math.,12(3),,,1929,387,408,Greek cube root of 3.,1,0,

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,29,19,0,0,0,0,Al-Daffa A.,Stroyls J.J.,,Studies in the Exact Sciences in Medieval Islam.,,,John Wiley and Sons,New York,1984,0,0,Arabic roots, ancient quadratics and cubics.,1,0,

,29,0,0,0,0,0,Lam L.-Y.,Ang T.-S.,,Fleeting Footsteps, Tracing the Conception of Arithmetic and Algebra in Ancient China.,,,World Scientific,Singapore,1992,0,0,Chinese roots.,1,0,

,20,0,0,0,0,0,Mignotte M.,Glesser P.,,On the smallest divisor of a polynomial.,J. Symb. Comp.,17,,,1994,277,282,Over integers.,1,0,

,20,0,0,0,0,0,Collins G.E.,Encarnación M.J.,,Improved techniques for factoring univariate polynomials.,J. Symb. Comp.,21,,,1996,313,327,Over integers.,1,0,

,18,21,0,0,0,0,da Silva A.P.,Sri Ranga A.,,Polynomials generated by a three term recurrence relation: bounds for complex zeros.,Lin. Alg. Appl.,397,,,2005,299,324,Title says it.,1,0,

,15,0,0,0,0,0,Hristov V.,Iliev A.I.,Kjurkchiev N.V.,A note on the convergence of nonstationary finite-difference analogues.,Comput. Math. Math. Phys.,45,,,2005,194,201,Based on Halley's method, may be very efficient.,1,0,

,19,0,0,0,0,0,Anbouba A.,,,Acquistion de l'algèbre par les Arabes et premiers développements. Apercu général.,J. Hist. Arabic Sci.,2,,,1978,66,100,Early quadratics.,1,0,

,19,0,0,0,0,0,Baqir T.,,,Some more mathematical texts from Tell Harmal.,Sumer,7,,,1951,28,45,Early quadratics.,1,0,

,19,0,0,0,0,0,Amir-Moéz A.R.,,,A paper of Omar Khayyam,Scripta Math.,26,,,1963,323,327,Cubic solved by conic sections.,1,0,

,19,0,0,0,0,0,Gandz S.,,,Studies in Babylonian Mathematics III: Isoperimetric Problems and the Origin of the Quadradic Equations.,Isis,32,,,1940,103,115,Early history of quadratic.,1,0,

,19,0,0,0,0,0,Goetsch H.,,,Die algebra der Babylonier.,Arch. Hist. Exact Sci.,5,,,1968,79,153,Early quadratics.,1,0,

,19,0,0,0,0,0,Karpinski L.C.,Winter J.G.,,Contributions to the History of Science.,,,U. of Michigan Press.,Ann Arbour,1930,0,0,Al-Khowarizmi's treatment of quadratics.,1,0,

,19,0,0,0,0,0,Kennedy E.S.,,,"The Exact Sciences" in The Cambridge History of Iran vol. IV ed. R.N. Frye. (Chapter 11),,,Cambridge U.P.,,1975,378,395,Very early quadratics.,1,0,

,13,29,0,0,0,0,Lay-Yong L.,,,The Chinese connection between the Pascal triangle and the solution of numerical equations of any degree.,Histora. Math.,7,,,1980,407,424,Horner's method and roots.,1,0,

,19,0,0,0,0,0,Levey M.,,,Abu Kamil,Dictionary of Scientific Biography,1,,,0,30,32,Low-degrees.,1,0,

,19,0,0,0,0,0,Levey M.,,,Some notes on the algebra of Abu Kamil Shuja: A fusion of Babylonian and Greek algebra.,L'Enseign. Math.,4,,,1958,77,92,Early quadratics.,1,0,

,29,0,0,0,0,0,van der Waerden B.L.,,,On Pre-Babylonian Mathematics I-II.,Arch. Hist. Exact Sci.,23,,,1980,1,25,Also pg. 27-46. Very early square roots.,1,0,

,19,0,0,0,0,0,Woepcke F.,,,Notice sur un manuscrit Arabe d'un traité d'algèbre par Aboul Fath Omar Ben Ibrahim Alkhayami, contenant la construction géométrique des équations cubiques.,J. reine angew Math.,40,,,1850,160,172,Solves cubics using conics.,1,0,

,3,12,0,0,0,0,Petkovic M.S.,Milosevic D.M.,,A new higher-order family of inclusion zero-finding methods.,J. Comput. Appl. Math,182,,,2005,416,432,4th order simultaneous inclusion method.,1,0,

,19,0,0,0,0,0,Prakash S.,,,A critical study of Brahmagupta and his works.,,,,New Delhi,1986,166,172,Earliest quadratic (AD 499),1,0,

,29,0,0,0,0,0,Rosenfeld B.,Youschkevitch A.,,al-Kashi,Dictionary of Scentific.Biography,7,,,1973,255,262,Square root of integers.,1,0,

,20,0,0,0,0,0,Niederreiter H.,Göttfert R.,,On a new factorization algorithm for polynomials over finite fields.,Math. Comp.,64,,,1995,347,353,No note.,1,0,

,20,0,0,0,0,0,Knopfmacher A.,,,Enumerating basic properties of polynomials over a finite field.,South African J. Sci.,91,,,1995,10,11,No note.,1,0,

,13,18,0,0,0,0,Granville A.,,,Bounding the Coefficients of a Divisor of a Given Polynomial.,Monat. Math.,109,,,1990,271,277,Gives bounds on coefficients of divisor.,1,0,

,19,25,0,0,0,0,Artemiadis N.K.,,,History of Mathematics.,Amer. Math. Soc.,,,,2004,0,0,Early quadratics & cubics; existence.,1,0,

,17,0,0,0,0,0,Smoktunowicz A.,Wrobel I.,,On improving the accuracy of Homer's and Goertzel's algorithms.,Numer. Algs.,38,,,2005,243,258,Improves stability of polynomial evaluation.,1,0,

,7,0,0,0,0,0,Sharma J.R.,,,A family of methods for solving non-linear equations using quadratic interpolation.,Computers Math. Applic.,48,,,2004,709,714,Uses no derivatives; order 1.84,1,0,

,30,0,0,0,0,0,Bini D.A.,Gemignani L.,,Solving quadratic matrix equations and factoring polynomials: new fixed point iterations based on Schur complements of Toeplitz matrices.,Numer. Lin. Alg. Appls.,12,,,2005,181,189,Uses matrices.,1,0,

,10,0,0,0,0,0,Corless R.M.,Watt S.M.,Lihong Z.,QR factoring to compute the GCD of univariate approximate polynomials.,IEEE Trans. Signal Proc.,52,,,2004,3394,3402,Title says it.,1,0,

,3,30,0,0,0,0,Zeng Z.,,,Computing multiple roots of inexact polynomials.,Math. Comp.,74,,,2005,869,903,Calculates multiple roots with high accuracy without using multiple precision. Uses singular values.,1,0,

,18,0,0,0,0,0,Kalantari B.,,,An infinite family of bounds on zeros of analytic functions and relationship to Smale's bound.,Math. Comp.,74,,,2005,841,852,Gives lower bounds on gap between distinct zeros of polynomials and lower & upper bounds on magnitudes of the roots.,1,0,

,3,0,0,0,0,0,Huang D.S.,Horace H.S.I.,Ken C.K.L. et al,A new partitioning neural network model for recursively finding arbitrary roots of higher order arbitrary polynomials.,Appl. Math. Comput.,162,,,2005,1183,1200,Uses neural network to achieve high speed.,1,0,

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,19,0,0,0,0,0,Smeur A.J.E.M.,,,The Rule of False applied to the quadratic equation, in three sixteenth century arithmetics.,Arch. Int. His. Sci.,28,,,1978,66,101,No note.,1,0,

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,21,0,0,0,0,0,Elbert A.,Muldoon M.E.,,On the derivative with respect to a parameter of a zero of a Sturm-Liouville function.,SIAM J. Math. Anal.,25,,,1994,354,364,Considers Gegenbauer polynomials.,1,0,

,25,0,0,0,0,0,Postnikov M.M.,,,Fundamentals of Galois Theory. Trans. L.F. Boron, Ed. R.A. Moore.,,,P. Noordhoff Ltd.,Groningen.,1962,0,0,Solution by radicals.,1,0,

,25,0,0,0,0,0,Rosen M.I.,,,Niels Hendrik Abel and the equation of the fifth degree.,Amer. Math. Monthly,102,,,1995,495,505,Non-solubility by radicals.,1,0,

,19,0,0,0,0,0,Gregory J.,,,James Gregory tercentenary memorial volume. Ed. H.W. Turnbull.,,,,London,1939,0,0,Treats up to quintic.,1,0,

,19,0,0,0,0,0,Scriba C.J.,,,Wallis and Harriot.,Centaurus,10,,,1964,248,257,No note.,1,0,

,19,25,0,0,0,0,van der Waerden B.L.,,,A history of algebra from al-Khwarizmi to Emmy Noether.,,,,Berlin,1985,0,0,Low-degree, existence, solution by radicals.,1,0,

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,19,0,0,0,0,0,Running T.R.,,,Graphical Mathematics.,,,Wiley,New York,1927,0,0,Treats low-degree graphically.,1,0,

,10,0,0,0,0,0,Thomas J.M.,,,Sturm's Theorem for Multiple Roots.,Nat. Math. Magazine,15,,,1941,391,394,Title says it.,1,0,

,19,0,0,0,0,0,Toti R.,,,Matematici Fiorentini del Tre-Quattrocento.,Symposia Math.,27,,,1983,3,21,Treats some special quadratics.,1,0,

,20,0,0,0,0,0,Abbott J.,Shoup V.,Zimmermann P.,Factorization in Z[x]: the searching phase.,Proc. ISSAC 2000,,,,2000,1,7,Accelerates searching phase of Berlekamp-Zassenhaus algorithm.,1,0,

,3,12,0,0,0,0,Petkovic M.S.,Milosevic D.,,Improved Hally-like methods for the inclusion of polynomial zeros.,Appl. Math. Comp.,169,,,2005,417,436,High-order interval methods.,1,0,

,3,12,0,0,0,0,Zhu L.,,,On the convergent conditions of Durand-Kerner in parallel circular iteration of multi-step.,Appl. Math. Comp.,169,,,2005,179,191,Describes a multi-step interval method of high order.,1,0,

,25,0,0,0,0,0,Lure B.B.,Gladkikh M.B.,,Unsolvability in radicals for a class of equations of degree five.,J. Math. Sci.,130,,,2005,4734,4734,No note.,1,0,

,2,0,0,0,0,0,Wu T.-M.,,,A study of convergence on the Newton-homotopy continuation method.,Appl. Math. Comput,168,,,2005,1169,1174,Title says it.,1,0,

,3,0,0,0,0,0,Zhu L.,,,On the convergent condition of Newton-like method in parallel circular iteration for simultaneously finding all multiple zeros of a polynomial.,Appl. Math. Comput.,168,,,2005,677,685,,1,0,

,3,12,0,0,0,0,Zhu L.,,,A modified Newton method in parallel circular iteration of single step and double step.,Comput. Math. Appl.,50,,,2005,1513,1524,Simultaneous interval method based on Ehrlich's.,1,0,

,2,0,0,0,0,0,Mamta et al.,,,On some third order iterative methods for solving nonlinear equations.,Appl. Math. Comput.,171,,,2005,272,280,Third order iterative methods without second derivatives.,1,0,

,7,0,0,0,0,0,Kanwar V.,Sharma J.R.,,A new family of Secant-like methods with superlinear convergence.,Appl. Math. Comput.,171,,,2005,104,107,No note.,1,0,

,1,0,0,0,0,0,Yakoubsohn J.-C.,,,Numerical analysis of a bisection-exclusion method to find zeros of univariate analytic functions.,J. Complexity,21,,,2005,652,690,No note.,1,0,

,10,0,0,0,0,0,Coste M. et al,,,Gereralized Budan-Fourier theorem and virtual roots.,J. Complexity,21,,,2005,479,486,No note.,1,0,

,17,0,0,0,0,0,Bostan A.,Schost E.E.,,Polynomial evaluation and interpolation on special sets of points.,J. Complexity,21,,,2005,420,446,Points form arithmetic or geometrical progression.,1,0,

,21,0,0,0,0,0,Area I. et al,,,Zeros of Jacobi functions of the second kind.,J. Comput. Appl. Math.,188,,,2006,65,76,No note.,1,0,

,25,0,0,0,0,0,Leibman G.,,,A nonstandard proof of the fundamental theorem of algebra.,Amer. Math. Monthly,112,,,2005,705,712,Proves existence using topology and nonstandard analysis.,1,0,

,3,30,13,0,0,0,Pan V.Y.,,,Coefficient-free adaptations of polynomial root-finders.,Computers Math. Applic.,50,,,2005,263,269,Uses evaluations of a polynomial without knowing its coefficients.,1,0,

,7,32,0,0,0,0,Wu T.-M.,,,A modified formula of ancient Chinese algorithm by the homotopy continuation technique.,Appl. Math. Comput.,165,,,2005,31,35,Combines Secant method with continuation.,1,0,

,1,7,0,0,0,0,Wu X.,,,Improved Muller method and Bisection method with global and asymptotic superlinear convergence of both point and interval for solving nonlinear equations.,Appl. Math. Comput.,166,,,2005,299,311,Method is globally convergent for real roots and has efficiency 1.84,1,0,

,18,0,0,0,0,0,Kalantari B.,,,Corrigendum to "An infinite family of bounds on zeros of analytic functions and realtionships to Smales bound",Math. Comput.,74,,,2005,2101,2101,Title says it.,1,0,

,28,0,0,0,0,0,Rahman Q.I.,Schmeisser G.,,Analytic Theory of Polynomials,,,Oxford UP,,2002,0,0,Mostly not numerical, but considers relation of zeros to that of derivative.,1,0,

,30,0,0,0,0,0,Pan V.Y.,,,The amended DSeSC power method for polynomial root finding.,Comput. Math. Appl.,49,,,2005,1515,1524,Finds eigenvalues of associated Frobenius matrix by repeated squaring. Very fast.,1,0,

,15,0,0,0,0,0,Grau M.,Peris J.M.,,Iterative method generated by inverse interpolation with additional evaluations.,Numer. Algorithms,40,,,2005,33,45,Uses up to n points and up to m'th derivative (low m & n in practice),1,0,

,2,0,0,0,0,0,Lakshmikantham V.,Vatsala A.S.,,Generalized quasilinearization versus Newton's method.,Appl. Math. Comput.,164,,,2005,523,530,Uses differential equation.,1,0,

,2,0,0,0,0,0,Mamta V.K.,Kukreja V.K.,Singh S.,On a class of quadratically convergent iteration formulae,Appl. Math. Comput.,166,,,2005,633,637,Generalizes Newton- much more robust than Newton.,1,0,

,3,0,0,0,0,0,Iliev A.,Kjurkchiev N.,,Some methods for simultaneous factorization of a part of all multiple roots of algebraic polynomials.,Computing,75,,,2005,85,97,Simultaneous methods of order 2 for multiple roots.,1,0,

,3,12,0,0,0,0,Petkovic M.S.,Milosevic D.,,Derivative-free inclusion methods for polynomial zeros.,Computing,75,,,2005,71,83,Simultaneous interval methods composed by combining lower-order methods.,1,0,

,3,12,0,0,0,0,Petkovic L.D.,Petkovic M.S.,Milosevic D.,Weierstrass-like methods with corrections for the inclusion of polynomial zeros.,Computing,75,,,2005,55,69,Simultaneous methods in circular arithmetic of increased order.,1,0,

,3,0,0,0,0,0,Petkovic M.S.,Rancic L.,,A new fourth-order family of simultaneous methods for finding polynomial zeros.,Appl. Math. Comput.,164,,,2005,227,248,Needs about 51/2 function evaluations, thus not very efficient. Considers multiple roots.,1,0,

,13,0,0,0,0,0,Pan V.Y.,,,"Univariate polynomials: nearly optimal algorithms for factorization and root-finding" in Int. Symp. Symbolic and Algebraic Computation. Ed. B. Mourrain.,ACM,,,London, Canada,2001,253,267,Uses recursive splitting.,1,0,

,2,0,0,0,0,0,Kanwar V.,,,A family of third-order multi-point methods for solving nonlinear equations.,Appl. Math. Comput.,176,,,2006,409,413,Variation on Newton is order 3 with 3 function evaluations.,1,0,

,15,0,0,0,0,0,Kanwar V.,Singh S.,Guha R.K. et al,On method of osculating circle for solving nonlinear equations.,Appl. Math. Comput.,176,,,2006,379,382,3rd order but uses 1st and 2nd derivatives.,1,0,

,2,0,0,0,0,0,Kou J.,Li Y.,Wang X.,On modified Newton method with cubic convergence.,Appl. Math. Comput.,176,,,2006,123,127,Cubic but 3 function evaluations.,1,0,

,7,13,0,0,0,0,Boyd J.P.,,,Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves.,Appl. Math. Comput.,174,,,2006,1642,1658,Interval subdivided and tested for zero using linear or cubic polynomial.,1,0,

,2,0,0,0,0,0,Ujevic N.,,,A method for solving nonlinear equations.,Appl. Math. Comput.,174,,,2006,1416,1426,Gives variations on Newton's method based on quadrature.,1,0,

,8,19,0,0,0,0,Abbasbandy S.,Jafarian A.,,Steepest descent method for solving fuzzy nonlinear equations.,Appl. Math. Comput.,174,,,2006,669,675,Gives low-order examples.,1,0,

,26,0,0,0,0,0,Rezvani N.,Corless R.M.,,The nearest polynomial with a given zero, revisited.,ACM Sigsam Bull.,39-3,,,2005,73,79,Title says it.,1,0,

,2,0,0,0,0,0,Lei T.,,,Branched coverings and cubic Newton maps.,Fund. Math.,154,,,1997,207,226,Julia sets considered,1,0,

,29,0,0,0,0,0,Levey M.,Petruck M.,,Kushyar ibn Labban: Principles of Hindu Reckoning. (A translation with introduction and notes),,,Madison,Wisconsin,1965,0,0,Early square roots.,1,0,

,3,12,0,0,0,0,Petkovic M.S.,Milosevic D.,,Ostrowski-like method with corrections for the inclusion of polynomial zeros.,Reliable Computing,10,,,2004,437,467,Simultaneous interval methods.,1,0,

,1,2,7,16,0,0,Stewart, G.W.,,,Afternotes on Numerical Analysis,,,SIAM,,1996,0,0,Covers bisection, Newton, Secant, Convergence,1,0,

,2,0,0,0,0,0,Milnor, J.,,,Dynamics in One Complex Variable,,,Vieweg,Braunschweig,1999,0,0,Fatou and Julia sets etc.,1,0,

,20,0,0,0,0,0,Rabinowitz, S.,,,The factorization of x⁵±x+n,Math. Mag.,61,,,1988,191,193,,1,0,

,19,0,0,0,0,0,Vogel, K.,,,Vorgriechische Mathematik. Vol. 2, Die mathematik der Babylonier,,,,Hanover,1959,0,0,Babylonian quadratics,1,0,

,21,0,0,0,0,0,Richardson, D.,,,Finding the number of distinct real roots of sparse polynomials of the form p(x,xⁿ) in "Computational Algebraic Geometry" (Nice 2002),,,Birkhauser,Boston,1993,225,233,,1,0,

,19,0,0,0,0,0,Folkerts, M.,,,Die älteste lateinische Schrift über das indische Rechnen nach al-Hwarizmi,Abh. Bayer. Akad. Wiss. Phil-hist Kl,N.S. 113,,,1997,0,0,Early quadratics,1,0,

,13,0,0,0,0,0,Plagianakos V.P.,Nousis N.K.,Vrahatis M.N.,Locating and computing in parallel all the simple roots of special functions using PVM.,J. Comput. Appl. Math.,133,,,2001,545,554,No note.,1,0,

,20,0,0,0,0,0,Panario D.,Gourdon X.,Flajolet P.,An analytic approach to smooth polynomials, in "Algorithmic Number Theory Symposium 1998",Lect. Notes in Comp. Sci.,1423,Springer-Verlag,New York/Berlin,1998,226,236,Considers factorization over finite fields.,1,0,

,20,0,0,0,0,0,Fleischmann P.,Roelse P.,,Comparitive implementations of Berlekamp's and Niederreter's polynomial factorization algorithms, in "Finite Fields and Applications." eds. S. Cohen & H. Niederreiter.,,,Cambrige Univ. Press,,1996,73,84,Considers factorization over finite fields.,1,0,

,20,0,0,0,0,0,Shparlinski I.E.,,,Finite Fields: Theory and Computation,,,Kluwer Academic P.,,1999,0,0,No note.,1,0,

,21,0,0,0,0,0,Li Z.,,,A subresultant theory for Ore polynomials with applications, in "Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC)",,,,,1998,132,139,No note.,1,0,

,1,2,7,26,0,0,Golub G.H.,Ortega J.M.,,Scientific Computing: An Introduction with Parallel Computing.,,,Academic Press,New York.,1993,0,0,Considers bisection, Newton, secant, and conditioning.,1,0,

,17,0,0,0,0,0,Smoktunowicz A.,,,Backward stability of Clenshaw's algorithm.,BIT,42,,,2002,600,610,Evaluation of series of orthogonal polynomials.,1,0,

,2,0,0,0,0,0,Simons S.,,,A modification of the Newton-Raphson method.,Math. Gaz.,90,,,2006,128,130,Method of implicit deflation.,1,0,

,15,0,0,0,0,0,Basto M. et al,,,A new iterative method to compute nonlinear equations.,Appl. Math. Comput.,173,,,2006,468,483,3rd order with 3 evaluations.,1,0,

,2,0,0,0,0,0,Grau M.,Diaz-Barrero J.L.,,An improvement to Ostrowski root-finding method.,Appl. Math. Comput.,173,,,2006,450,456,Method of order 4 with 3 evalutations.,1,0,

,20,29,0,0,0,0,Kong F. et al,,,Improved generalized Atkin algorithm for computing square roots in finite fields.,Inform. Proc. Lett.,98,,,2006,1,5,Title says it.,1,0,

,31,0,0,0,0,0,Abbaoui K.,Cherrualt Y.,,Convergence of Adomian's method applied to nonlinear equations.,Mathl. Comput. Modelling,20-9,,,1994,69,73,Solution in series.,1,0,

,1,2,7,16,17,26,Eldén L.,Wittmeyer-Koch L.,,Numerical Analysis: An Introduction,,,Academic Press,New York,1993,0,0,Treats bisection, Newton, Secant, convergence, errors, evaluation, square root.,1,0,

,19,0,0,0,0,0,Anglin W.S.,,,Mathematics: A Concise History and Philosophy,,,Springer-Verlag,,1994,0,0,Treats history of cubic.,1,0,

,29,,,,,,Eldén L.,Wittmeyer-Koch L.,,Numerical Analysis: An Introduction,,,Academic Press,New York,1993,0,0,Treats bisection, Newton, Secant, convergence, errors, evaluation, square root.,1,0,

,29,0,0,0,0,0,Kornerup P.,Muller J.-M.,,Choosing starting values for certain Newton-Raphson iterations,Theor. Comput. Sci.,351,,,2006,101,110,Best starting points for square root algorithm,1,0,

,20,0,0,0,0,0,Abu Salem F.K.,,,A New Sparse Gaussian Elimination Algorithm and the Niederreiter Linear System for Trinomials over F₂,Computing,77,,,2006,179,203,Concerns factorization of sparse polynomials over F₂,1,0,

,2,0,0,0,0,0,Sharma J.R.,,,A composite third-order Newton-Steffensen method for solving nonlinear equations,Appl. Math. Comput.,169,,,2005,242,246,Succeeds where Newton or Steffensen separately fail. Efficiency $\sqrt[3]{} 3$ ,1,0,

,2,0,0,0,0,0,Chun C.,,,Iterative Methods Improving Newton's Method by the Decomposition Method,Comput. Math. Applic.,50,,,2005,1559,1568,Methods of efficiency log $\sqrt[3]{} 3, \log$ $\sqrt[4]{} 4, \log$ $\sqrt[5]{} 5 requiring less high derivatives than usual .$ ,1,0,

,1,7,0,0,0,0,Boyd J.P.,,,Computing real roots of a polynomial in Chebyshev series form through subdivison.,Appl. Numer. Math.,56,,,2006,1077,1091,Applies low-degree interpolation over many subintervals.,1,0,

,11,0,0,0,0,0,Borobia A.,Domido S.,,Three coefficients of a polynomial can determine its φ-instability.,Lin. Alg. Appls.,416,,,2006,857,867,Determines if roots in a wedge in 3rd and 4th quadrant.,1,0,

,3,23,0,0,0,0,Mourrain B. et al,,,Determining the number of real roots of polynomials through neural networks.,Comput. Math. Applics.,51,,,2006,527,536,For low-degree- faster than conventional methods.,1,0,

,10,0,0,0,0,0,Yan C.-D.,Chieng W.-H.,,Method for finding multiple roots of polynomials.,Comput. Math. Appls.,51,,,2006,605,620,Uses GCD of polynomial and its derivative.,1,0,

,13,0,0,0,0,0,Stetter H.J.,,,Numerical Polynomial Algebra,,,SIAM,Philadelphia PA,2004,0,0,No note.,1,0,

,18,0,0,0,0,0,Schmeisser G.,,,Nullstelleneinschliessungen und Landau-Fejer-Montel Problem,Studia Sci. Math. Hung.,7,,,1972,459,472,,1,0,

,26,0,0,0,0,0,Beauzamy B.,,,How the roots of a polynomial vary with its coefficients: a local quantitative result.,Canad. Math. Bull.,42,,,1999,3,12,Sensitivity to perturbations in the coefficients.,1,0,

,30,0,0,0,0,0,Bini D.A.,Gemignani L.,Pan V.Y.,Fast and stable QR eigenvalue algorithms for generalized companion matrices and secular equations.,Numer. Math.,100,,,2005,373,408,Fast matrix method.,1,0,

,30,0,0,0,0,0,Bini D.A.,Daddi E.,Gemignani L.,On the shifted QR iteration applied to companion matrices.,Electr. Trans. Numer. Anal.,18,,,2004,137,152,,1,0,

,13,0,0,0,0,0,Hoteit L.,,,FFT-based fast polynomial rooting.,Proc. ICASSP' 2000,6,,,2000,3315,3318,Uses FFT for moderate to high degree.,1,0,

,2,0,0,0,0,0,Steiglitz K.,Dickinson B.,,Phase unwrapping by factorization,IEEE Trans. Acoust. Speech Signal Process,30,,,1982,984,991,Uses Newton.,1,0,

,23,0,0,0,0,0,Huang D.S.,Horace H.S. Ip,Chi Z. et al,Dilation method for finding close roots of polynomials based on constrained learning neural networks.,Phys. Lett. A.,309 (5-6),,,2003,443,451,Uses neural networks.,1,0,

,23,0,0,0,0,0,Huang D.S.,Chi Z.,,Finding complex roots of polynomials by feedforward neural networks, in "2001 Int. Joint Conf. On Neural Networks (IJCNN2001)" Addendum,,,,Washington DC,2001,13,18,Uses neural networks.,1,0,

,23,0,0,0,0,0,Huang D.S.,Chi Z.,,Neural networks with problem decomposition for finding real roots of polynomials, in "2001 Int. Joint Conf. On Neural Networks (IJCNN2001)" Addendum,,,,Washington DC,2001,25,30,Uses neural networks.,1,0,

,1,2,7,0,0,0,Allen M. III,Issacson E.,,Numerical Analysis for Applied Science.,,,John Wiley,New York.,1998,0,0,Treats bisection, Newton, and secant.,1,0,

,20,0,0,0,0,0,Driver E.,Leonard P.A.,Williams K.S.,Irreducible quartic polynomials with factorizations Module p,Amer. Math. Monthly,112,,,2005,876,890,Over finite fields.,1,0,

,21,0,0,0,0,0,Zemyan S.M.,,,On the zeros of the Nth partial sum of the exponential series,Amer. Math. Monthly,112,,,2005,891,909,Title says it.,1,0,

,18,0,0,0,0,0,Kim S.-H.,,,On the moduli of the zeros of a polynomial,Amer. Math. Monthly,112,,,2005,924,925,A priori bounds on roots.,1,0,

,13,24,0,0,0,0,Nedzhibov G.H.,,,An acceleration of iterative processes for solving nonlinear equations.,Appl. Math. Comput.,168,,,2005,320,332,Applies to multiple roots also.,1,0,

,26,0,0,0,0,0,Graillat S.,,,A note on the nearest polynomial with a given root.,ACM SIGSAM Bull.,39-2,,,2005,53,60,Sensitivity. Related to pseudospectra.,1,0,

,15,0,0,0,0,0,Grau M.,Diaz-Barrero J.L.,,An improvement of the Euler-Chebyshev iterative method.,J. Math. Anal. Appl.,315,,,2006,1,7,Appears to give a 5th order method with 3 function evalutaions.,1,0,

,17,0,0,0,0,0,Barno R.,Pe Ata J.M.,,Evaluation of the derivative of a polynomial in Bernstein form.,Appl. Math. Comp.,167,,,2005,125,142,Title says it.,1,0,

,31,32,0,0,0,0,Abbasbandy,,,Modified homotopy perturbation method for nonlinear equations and comparison with Adomian decomposition method.,Appl. Math. Comput.,172,,,2006,431,438,Title says it.,1,0,

,32,0,0,0,0,0,Wu T.-M.,,,A new formula of solving nonlinear equations by Adomian and homotopy methods.,Appl. Math. Comput.,172,,,2006,903,907,Title says it.,1,0,

,2,0,0,0,0,0,Xingyuan W.,Liu W.,,The Julia set of Newton's method for multiple roots.,Appl. Math. Comput.,172,,,2006,101,110,Region from which Newton converges.,1,0,

,2,0,0,0,0,0,Luo X.-G.,,,A note on the new iteration method for solving algebraic equations.,Appl. Math. Comput.,171,,,2005,1177,1183,A new method is not a good as claimed.,1,0,

,30,0,0,0,0,0,Pan V.,,,Polynomial root-finding with matrix eigen-solving,ACM Sigsam Bull.,39-3,,,2005,87,87,Contains abstract only. Not many details.,1,0,

,10,0,0,0,0,0,Krandick W.,Meilhorn K.,,New bounds for the Descartes method.,ACM Sigsam Bull.,39-3,,,2005,94,94,Gives bounds for number of subdivisions in Descartes' method for real roots.,1,0,

,7,0,0,0,0,0,Feng X.,He Y.,,Parametric iterative methods of second order for solving nonlinear equations.,Appl. Math. Comput.,173,,,2006,1060,1067,2nd order without derivatives.,1,0,

,15,0,0,0,0,0,Fang T.,Guo F.,Lee C.F.,A new iteration method with cubic convergence to solve nonlinear algebraic equations.,Appl. Math. Comput.,175,,,2006,1147,1155,Uses 2nd derivative.,1,0,

,29,0,0,0,0,0,Ozban A.Y.,,,New methods for approximating square roots.,Appl. Math. Comput.,175,,,2006,532,540,High order methods for square roots competitive with existing ones.,1,0,

,28,30,0,0,0,0,Cheung W.S.,Ng T.W.,,A companion matrix approach to the study of zeros and critical points of a polynomial.,J. Math. Anal. Appl.,319,,,2006,690,707,Relation between roots of a polynomial and its derivative.,1,0,

,21,0,0,0,0,0,Krasikov I.,,,On extreme zeros of classical orthogonal polynomials.,J. Comput. Appl. Math.,193,,,2006,168,182,Title says it.,1,0,

,1,26,0,0,0,0,Sikorski K.A.,,,Optimal Solution of Nonlinear Equations.,,,Oxford UP,,2001,0,0,Deals with complexity, bisection method.,1,0,

,25,0,0,0,0,0,Körner T.,,,On the fundamental theorem of algebra,Amer. Math. Monthly,113,,,2006,347,348,Proof of existence.,1,0,

,25,0,0,0,0,0,Burckel R.B.,,,Fubinito (immediately) implies FTA,Amer. Math. Monthly,113,,,2006,344,346,Proof of existence.,1,0,

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,23,0,0,0,0,0,Abbasbandy S.,Otadi M.,,Numerical solution of fuzzy polynomials by fuzzy neural networks.,Appl. Math. Comp.,181,,,2006,1084,1089,Title says it.,1,0,

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,15,0,0,0,0,0,Biazar J.,Amirteimoori A.,,An improvement to the fixed-point iteration.,Appl. Math. Comp.,182,,,2006,567,571,Uses very high derivatives.,1,0,

,15,0,0,0,0,0,Abu-Alshaikh I.,Sahin A.,,Two-point iterative methods for solving non-linear equations.,Appl. Math. Comp.,182,,,2006,871,878,Uses second derivative. Not clear what order is.,1,0,

,15,0,0,0,0,0,Chen J.,,,Some new iterative methods with three-order convergence.,Appl. Math. Comp.,181,,,2006,1519,1522,Third order but uses second derivative.,1,0,

,2,0,0,0,0,0,Kou J.,Li Y.,Wang X.,A modification of Newton method with third-order convergence.,Appl. Math. Comp.,181,,,2006,1106,1111,Two-step method with third order and 3 function evaluations per iteration.,1,0,

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,7,0,0,0,0,0,Lam L.Y.,,,Yang Hui's commentary on the ying nu chapter of the Chiu Chang Suan Shu,Hist. Math.,1,,,1974,47,64,Early regual falsi,1,0,

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,28,0,0,0,0,0,Berloty Le P.,,,Sur les équations algébriques.,Comp. Ren. Acad. Sci.,99,,,1884,745,747,Zeros of a polynomial and its derivatives.,1,0,

,18,0,0,0,0,0,Bendixson I.,,,Sur les racines d'une équation fondamentale,Acta Math.,25,,,1902,359,365,Bounds on imaginary parts of eigenvalues of non-symetric matrix,1,0,

,28,0,0,0,0,0,Biernacki M.,,,Sur les zéros des polynômes et sur les fonctions entières dont le développment taylorien présente des lacunes.,Bull. Sci. Math. Ser. 2,69,,,1945,197,203,No note.,1,0,

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,15,0,0,0,0,0,Noor M.A.,Noor K.I.,,Some iterative methods for nonlinear equations.,Appl. Math. Comput.,183,,,2006,774,779,Gives a 3-step composite method with 3 evaluations and 4th order. Uses 2nd derivative.,1,0,

,2,0,0,0,0,0,Kou J.,Li Y.,Wang X.,Modified Halley's method free from second derivative.,Appl. Math. Comput.,183,,,2006,704,708,3rd order with 3 evaluations.,1,0,

,10,0,0,0,0,0,Li Y.-B.,,,A new approach for constructing subresultants.,Appl. Math. Comput.,183,,,2006,471,476,No note.,1,0,

,2,0,0,0,0,0,Noor M.A.,Noor K.I.,,Three-step iterative methods for nonlinear equations.,Appl. Math. Comput.,183,,,2006,322,327,Uses 3 evaluations to give 3rd order.,1,0,

,2,0,0,0,0,0,Noor M.A.,Noor K.I.,Khan W.A. et al,On iterative methods for nonlinear equations.,Appl. Math. Comput.,183,,,2006,128,133,Generalized Newton with 2 sub-steps per iteration. Not very efficient.,1,0,

,29,19,25,0,0,0,Lam L.Y.,,,Chinese Polynomial Equations in the Thirteenth Century, in "Explorations in the History of Science and Technology" eds Li Guoliao et al.,,,Shanghai Chinese Classics,Shanghai,1982,231,272,Surds, low-degrees, mechanical aids.,1,0,

,29,0,0,0,0,0,Lam L.Y.,,,Jiu Zhang Suanshu (Nine chapters on the mathematical art: an overview),Arch. Hist. Exact Sci.,47-1,,,1996,1,51,Treats square and cube roots.,1,0,

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,25,19,0,0,0,0,Scott J.F.,,,The Mathematical Work of John Wallis.,,,,London,1938,0,0,Considers number of roots, solution of cubic.,1,0,

,19,29,0,0,0,0,Sen S.N.,,,Mathematics, in "A Consise History of Science in India" ed. D.M. Bose et al.,,,Indian National Sci. Acad,New Delhi,1978,136,212,Treats quadratic and surds.,1,0,

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,11,0,0,0,0,0,Lehnigk S.H.,,,Liapunov's direct method and the number of zeros with positive real parts of a polynomial with constant complex coefficients.,Zeit. Ang. Math. Mech.,47,,,1967,62,64,No note.,1,0,

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,10,0,0,0,0,0,Pan V.Y.,,,Approximate polynomial GCDs, Padé approximation, polynomial zeros, and bipartite graphs, in "Proc. 9th Ann. ACM-SIAM Symp.on Discrete Algorithms",,,ACM Press, SIAM Pub.,New York and PA,1998,68,77,Title says it.,1,0,

,7,0,0,0,0,0,Wu X.,,,Error analysis of a new transformation for multiple zeros finding free from derivative evaluations.,Comput. Math. Appl.,46 (8-9),,,2003,1195,1200,Title says it.,1,0,

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,31,0,0,0,0,0,Bini D.A.,Gemignani L.,Pan V.Y.,Inverse power and Durand/Kerner iteration for univariate polynomial root-finding.,Comp. Math. Appl.,47(2/3),,,2004,447,459,Uses matrices.,1,0,

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,15,0,0,0,0,0,Noor M.A.,,,New iterative schemes for nonlinear equations.,Appl. Math. Comput.,187,,,2007,937,943,Uses 2nd derivative.,1,0,

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,20,0,0,0,0,0,Salkind C.T.,,,Factorization of $a^{2n}$ + $a^{n} +1$ ,Math. Magazine,38,,,1965,163,163,a is an integer,1,0,

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,15,0,0,0,0,0,Osada N.,,,A one parameter family of locally quartically convergent zero-finding methods.,J. Comput. Appl. Math.,205,,,2007,116,128,4th order with 4 evaluations. Same efficiency as Newton. Involves several derivatives.,1,0,

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,15,0,0,0,0,0,Chun C.,,,A note on fifth-order iterative methods for solving nonlinear equations.,Appl. Math. Comput.,189,,,2007,1805,1807,A method of Noor and Noor has only third-order, not fifth.,1,0,

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,2,0,0,0,0,0,Chun C.,,,Certain improvements of Chebyshev-Halley methods with accelerated fourth-order convergence.,Appl. Math. Comput.,189,,,2007,597,601,4th order with 3 evaluations (1 function, 2 first derivatives).,1,0,

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,13,0,0,0,0,0,Turan, P.,,,To the analytic theory of algebraic equations,Bulgar. Akad. Nauk. Otdel. Mat. Fiz. Nauk. Izv.,3,,,1959,123,137,No Note,1,0,

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,2,0,0,0,0,0,Wang, X.,Kou, J.,Li, Y.,A variant of Jarratt method with sixth-order convergence,Appl. Math. Comput.,204,,,2008,14,19,Sixth order with 4 evaluations,1,0,

,19,0,0,0,0,0,Rechtschaffen, E.,,,Real roots of cubics: explicit formula for quasi-solutions,Math. Gaz.,92,,,2008,268,276,Title says it,1,0,

,2,0,0,0,0,0,Parhi, S. K.,Gupta, D. K.,,A sixth order method for nonlinear equations,Appl. Math. Comput.,203,,,2008,50,53,6th order with 4 evaluations, using first derivative only,1,0,

,2,0,0,0,0,0,Bi, W.,Ren, H.,Wu, Q.,New family of seventh-order methods for nonlinear equations,Appl. Math. Comput.,203,,,2008,408,412,7th order with 4 evaluations using only 1st order derivatives,1,0,

,15,0,0,0,0,0,Zhou, X.,,,Modified Chebyshev-Halley methods free from second derivative,Appl. Math. Comput.,203,,,2008,824,827,Third order with three evaluations, including only 1st derivatives,1,0,

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,2,0,0,0,0,0,Vy, D. T.,,,A fifth order iterative method for solving equations,Acta. Math. Hungar.,49,,,1987,129,137,Fifth order with 4 evaluations,1,0,

,25,0,0,0,0,0,Abian, A.,Wilson, J.A.,,A theorem equivalent to the fundamental theorem of algebra,Nieuw. Arch. Wiskunde ief voor,(4) 8,,,1990,47,48,Existence,1,,

,25,0,0,0,0,0,Boas, R. P.,,,A proof of the fundamental theorem of algebra,Amer. Math. Monthly.,42,,,1935,501,502,Existence,1,0,

,25,0,0,0,,0,Boas, R. P.,,,Yet another proof of the fundamental theorem of algebra,Amer. Math. Monthly.,71,,,1964,180,0,Existence,1,0,

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,19,0,0,0,0,0,Franci, R.,,,Contributi alla risoluzione dell'equazione di 3 grado nel XIV secolo, in "Mathemata, Festschrifte fur Helmut Gericke",,,Franz Steiner Verlag,Stuttgart,1984,221,228,Treats simple cubics (not general case),1,0,

,19,0,0,0,0,0,Woepke, F.,,,Extrait du Fakhri,,,A l'Imprimerie Imperiale,Paris,0,0,0,Eary treatment of quadratic,1,0,

,25,0,0,0,0,0,Bishop, E.,Bridges, D.,,Constructive analysis,,,Springer Verlag,Berlin,1985,0,0,Existence,1,0,

,18,0,0,0,0,0,Herzberger, J.,,,Construction of bounds for the positive root of a general class of polynomials with applications, in Inclusion Methods for nonlinear problems with applications in engineering, economics and Physiscs,Comput. Suppl.,16,Springer,Vienna,2003,0,0,Bounds on positive root of polynomials determining convergence order,1,0,

,10,0,0,0,0,0,Emiris, I. Z.,Mourrain, B.,Tsigaridas, E. P.,Real algebraic numbers: Complexity analysis and experimentation, in "Reliable Implementation of Real Number Algorithms etc.", eds P. Hertling et al (LNCS 5045),.,,Springer,,2006,0,0,No Note,1,0,

,2,0,0,0,0,0,Weerakoom, S.,Fernando, T. G. I.,,A variant of Newton's method with accelerated third-order convergence,Appl. Math. Lett.,13(8),,,2000,87,93,Third order with 3 evaluations,1,0,

,7,0,0,0,0,0,Wu, X.-Y.,Fu, D.,,New high-order convergence iteration methods without employing derivatives for solving nonlinear equations,Comput. Math. Applic.,41 (3/4),,,2001,489,495,No note,1,0,

,7,0,0,0,0,0,Iyengar, S. R. K.,Jain, R. K.,,Derivative free multipoint iterative methods for simple and multiple roots,BIT,26,,,1986,93,99,For multiple roots, 4th order method with 8 evaluations,1,0,

,13,29,2,15,0,0,Bailey, D. F.,,,A historical survey of solution by functional iteration,Mathematics Magazine,62,,,1989,155,166,Mentions Newton & Halley, n'th roots,1,0,

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,29,0,0,0,0,0,Hernandez, M. A.,Romero, N.,,High order algorithms for approximating nth roots,Int. Journal. Comput. Math.,81,,,2004,1001,1014,Derives general method of q'th order(q>=2), with Newton for q=2 & chebyshev for q=3,1,0,

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,10,0,0,0,0,0,Collins, G. E.,Loos, R.,,Real zeros of polynomials, in "Computer Algebra: Symbolic and Algebraic Computation", eds Buchberger et al,,,Springer-Verlag,Wien,1982,83,94,Uses Sturm, Descartes rule.,1,0,

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,18,12,0,0,0,0,Hertz, D.,Adjiman, C. S.,Floudas, C. A.,Two results on bounding the roots of interval polynomials,Comput. Chem. Eng.,23,,,1999,1333,1339,Title says it,1,0,

,19,0,0,0,0,0,Suter, H.,,,Die Mathematiker und Astronomen der Araber und ihre Werke,,,Leipzig,Teubner,1900,0,0,No Note,1,0,

,19,0,0,0,0,0,Dold-Samplonius, Y.,,,Developments in the solution to the equation cx² + bx = a from al-Khwarizmi to fibonacci, in: "Festschrift for E.S. Kennedy",,,New York AcademySciences,New York,1987,52,61,No Note,1,0,

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,2,0,0,0,0,0,Bi, W.,Ren, H.,Wu, Q.,Three-step iterative methods with eighth-order convergence for solving nonlinear equations,J. Comput. Appl. Math.,225,,,2009,105,112,8th order with 4 evaluations,1,0,

,2,0,0,0,0,0,Chun, C.,Bai, H. J.,Neta, B.,New families of nonlinear third-order solvers for finding multiple roots,Comput. Math. Applic.,57,,,2009,1574,1582,3rd order with 3 evaluations,1,0,

,15,0,0,0,0,0,Grau-Sanchez, M.,Diaz-Banero, J. L.,,Some sixth-order zero-finding variants of Chebyshev-Halley methods,Appl. Math. Comput.,211,,,2009,108,110,6th order with 4 evaluations,1,0,

,2,0,0,0,0,0,Grau-Sanchez, M.,Noguera, M.,Diaz-Banero, J. L.,Adams-like techniques for zero-finding methods,Appl. Math. Comput.,211,,,2009,130,136,Order 1+ $\sqrt{2}$ with 2 evaluations,1,0,

,2,0,0,0,0,0,Chun, C.,Neta, B.,,A third-order modification of Newton's method for multiple roots,Appl. Math. Comput.,211,,,2009,474,479,Third order with 3 evaluations for multiple roots,1,0,

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,10,20,0,0,0,0,Nagasaka, K.,,,Approximate polynomial GCD over the integers,SIGSAM Bull,42,,,2008,124,126,Title says it,1,0,

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,,0,0,0,0,0,Maheshwari, A. K.,,,A fourth order iterative method for solving nonlinear equations,Appl. Math. Comput.,211,,,2009,383,391,Fourth order with 3 evaluations,1,0,

,2,0,0,0,0,0,Wang, X.,Liu, L.,,Two new families of sixth-order methods for solving non-linear equations,Appl. Math. Comput.,213,,,2009,73,78,Sixth order with 4 evaluations,1,0,

,2,12,0,0,0,0,Nikas, L. A.,Graspa, T. N.,,Bounding the zeros of an interval equation,Appl. Math. Comput.,213,,,2009,466,478,Interval-based Newton method,1,0,

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,2,0,0,0,0,0,Zhou, X.,,,A note on "Some higher-order modifications of Newton's method for solving nonlinear equations",Appl. Math. Comput.,208,,,2009,0,0,Refers to method generalizing Newton; the original article has errors,1,0,

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,3,0,0,0,0,0,Ikhile, M. N. O.,,,An iterative method for simultaneous inclusion of polynomial zeros,J. Nig. Ass. Math. Phys.,5,,,2001,19,36,No Note,1,0,

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,3,0,0,0,0,0,Petkovic, L. D.,Petkovic, M. S.,Milosevic, D.,Inclusion Weierstrass-like root-finders with corrections,Filomat,17,,,2003,143,154,No Note,1,0,

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,3,0,0,0,0,0,Rancic, L. Z.,Petkovic, M. S.,,Square-root families for the simultaneous approximation of polynomial multiple zeros,Novi. Sad. J. Math.,35 (1),,,2005,59,70,Order 5 or 6,1,0,

,12,0,0,0,0,0,Sekigawa, H.,Shirayanagi, K.,,Locating real multiple zeros of a real interval polynomial,In: Proc. 2006 Int. Symp. Sym. Alg. Comp. ISSAC'06,,,,2006,310,317,Title says it,1,0,

,12,0,0,0,0,0,Sekigawa, H.,Shirayanagi, K.,,On the location of zeros of an interval polynomial, in "Symbolic-Numeric Computation", Eds D. Wang & L. Zhi,,,Birkhauser,,2007,167,184,Title says it,1,0,

,0,0,0,0,0,0,Lagrange, J. L.,,,Additions to Euler's Algebra,,1(1),,,0,0,0,Republished in vol. 7 of Lagrange's Oeuvres and vol. 1(1) of Euler's Opera (3.3),1,0,

,0,0,0,0,0,0,Poincare, H.,,,L'Oeuvre Mathematique de Weierstrass,Acta Mathematica,22,,,1899,1,18,(Preface),1,0,

,0,0,0,0,0,0,Hensel, K.,Landsberg, G.,,Theorie der algebraischen Funktionen einer Variabeln,,,Chelsea Reprint,,1965,,0,,1,0,

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,21,0,0,0,0,0,Yakimiw, E.,,,Accurate computation of weights in classical Gauss-Christoffel quadrature rules,J. Comput. Phys.,129,,,1996,406,430,High-order methods for zeros of some special polynomials,1,0,

,12,17,0,0,0,0,Hansen, E. R.,,,Sharpness in Interval Computations,Reliable Computing,3(1),,,1997,17,29,Considers evaluation of a polynomial over an interval,1,0,

,2,0,0,0,0,0,Wu, X.,,,A significant improvement on Newton's iterative method.,Appl. Math. Mech.,20,,,1999,924,927,Removes vestriction f'(x) ≠ 0,1,0,

,15,0,0,0,0,0,Buff, X.,Henriksen, C.,,On the Konig root-finding algorithms,Nonlinearity,16,,,2003,989,1015,Uses high derivatives,1,0,

,15,0,0,0,0,0,Hernandez, M. A.,,,A family of Chebyshev-Halley type methods,Internat. J. Comput. Math.,47,,,1992,59,63,Uses 2nd derivative, is at least 3rd order,1,0,

,2,15,0,0,0,0,Wang, X. Y.,Yu, X. J.,,Julia sets for the standard Newton's method, Halley's method and Schroder's method,Appl. Math. Comput.,189,,,2007,1186,1195,Fractals,1,0,

,3,0,0,0,0,0,Petkovic, M. S.,Petkovic, L. D.,,On a cubically convergent derivative free root finding method,Int. J. Comput. Math.,84,,,2007,505,513,Third order with 3 evaluations,1,0,

,10,0,0,0,0,0,Diaz-Toca, G.,Gonzalez-Vega, L.,,Various new expressions for subresultants and their applications,Appl. Alg. Eng. Comm. Comput.,15,,,2004,233,266,No note,1,0,

,21,0,0,0,0,0,Beardon, A. F.,Driver, K. A.,,The zeros of linear combinations of orthogonal polynomials,J. Approx. Theory,137,,,2005,179,186,No note,1,,

,21,0,0,0,0,0,Mastroianni, G.,Occorsio, D.,,Interlacing properties of the zeros of the orthogonal polynomials and approximation of the Hilbert transform,Comput. Math. Appl.,30(3-6),,,1995,155,168,No note,1,0,

,21,0,0,0,0,0,Mastroianni, G.,Occorsio, D.,,Optimal systems of nodes for Lagrange Interpolation on bounded intervals. A survey.,J. Comput. Appl. Math.,134,,,2001,325,341,No note,1,0,

,7,0,0,0,0,0,Shacham, M.,,,An improved memory method for the solution of a nonlinear equation,Chem. Eng. Sci.,44,,,1989,1495,1501,A multipoint secant method,1,0,

,2,5,7,0,0,0,Yun, B. I.,Petkovic, M. S.,,Iterative methods based on the signum function approach for solving nonlinear equations,Numer. Algor.,52,,,2009,649,662,Uses integration, Newton, secant etc,1,0,

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,2,0,0,0,0,0,Thukral, R.,Petkovic, M. S.,,A family of three-point methods of optimal order for solving nonlinear equations,J. Comput. Appl. Math.,233,,,2010,2278,2284,Order 8 with 4 evaluations,1,0,

,2,7,20,0,0,0,Bach, E.,,,Iterative root approximation in p-adic numerical analysis,J. Complexity,25,,,2009,511,529,Treats integer coefficients Mod p. Finds methods more efficient than Newton or Secant,1,0,

,21,0,0,0,0,0,Driver, K.,Jordaan, K.,,Zeros of linear combinations of Laguerre polynomials from different sequences,J. Comput. Appl. Math.,233,,,2009,719,722,No note,1,0,

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,2,7,0,0,0,0,Geum, Y. H.,Kim, Y. I.,,Cubic convergence of parameter-controlled Newton-secant method for multiple zeros,J. Comput. Appl. Math.,233,,,2009,931,937,3rd order with 3 evaluations for multiple zeros,1,0,

,19,0,0,0,0,0,Rashed, R.,,,Al-Kharizmi: The Beginnings of Algebra, Ed. & trans.,Saqi,,,,2009,0,0,Early quadratics,1,0,

,30,0,0,0,0,0,Bini, D. A.,Boito, P.,Eidelman, Y. Et al,A fast implicit QR eigenvalue algorithm for companion matrices,Lin. Alg. Appls.,432,,,2010,2006,2031,Title says it,1,0,

,2,0,0,0,0,0,Ren, M.,Wu, Q.,Bi, W.,New variants of Jarratt's method with sixth-order convergence,Numer. Algor.,52,,,2009,585,603,6th order with 4 evaluations,1,0,

,2,3,0,0,0,0,Petkovic, M. S.,,,The self-validated method for polynomial zeros of high efficiency,J. Comput. Appl. Math.,233,,,2009,1175,1186,Simultaneous method of order 6,1,0,

,15,0,0,0,0,0,Petkovic, M. S.,,,A remark on He's variational iteration technique for solving nonlinear equations,J. Comput. Appl. Math.,233,,,2009,1187,1189,Schroeder re-discovered,1,0,

,15,0,0,0,0,0,Petkovic, M. S.,Petkovic, L. D.,Hereg, D. H.,On Schroder's families of root-finding methods,J. Comput. Appl. Math.,233,,,2010,1755,1762,Many methods are in fact equivilent to Schroder's method,1,0,

,2,0,0,0,0,0,Li, S. G.,Cheng, L. Z.,Neta, B.,Some fourth-order nonlinear solvers with closed formulas for multiple roots,Comput. Math. Applic.,59,,,2010,126,135,4th order with 3 evaluations for multiple roots,1,0,

,2,0,0,0,0,0,Geum, Y. H.,Kim, Y. I.,,A multi-parameter family of three-step eighth-order iterative methods locating a simple root,Appl. Math. Comput.,215,,,2010,3375,3382,8th order with 4 evaluations,1,0,

,0,0,0,0,0,7,Kim, Y. I.,,,A new two-step biparametic family of sixth-order iterative methods free from second derivatives for solving nonlinear algebraic equations,Appl. Math. Comput.,215,,,2010,3418,3424,Efficiency $6^{1/4}$ ,1,0,

,2,0,0,0,0,0,Li, X.,Mu, C.,Ma, J.,Sixteenth-order method for nonlinear equations,Appl. Math. Comput.,215,,,2010,3754,3758,Efficiency $16^{1/6}$ ,1,0,

,2,0,0,0,0,0,Liu, L.,Wang, X.,,Eighth-order methods with high efficiency index for solving nonlinear equations,Appl. Math. Comput.,215,,,2010,3449,3454,Effficiency $8^{1/4}$ ,1,0,

,21,0,0,0,0,0,Krasikov, I.,,,Bounds for zeros of the Charlier polynomials,Methods Appl. Anal.,9 (4),,,2002,599,610,No note,1,0,

,18,21,0,0,0,0,Krasikov, I.,,,Bounds for zeros of the Laguerre polynomials,J. Approx. Theory,121,,,2003,287,291,Title says it,1,0,

,28,0,0,0,0,0,Tannaka, T.,,,Ein Satz uber die algebraischen Gleichungen,Tohoku Mathematical Journal,33,,,1931,187,189,Treats roots of second derivative,1,0,

,10,0,0,0,0,0,Tietze, H.,,,Uber eine Verallgemeinerung der Vorzeichenregeln von Descartes und Budan-Fourier.,Sitzung. Math. Naturwiss. Abt.. Bayer. Akad. Wiss.,,,,1935,357,377,No note,1,0,

,10,0,0,0,0,0,Tietze, H.,,,Uber die Vorzeichenregeln von Descartes und Budan-Fourier,Monatshefte fur Mathemetik und Physik,43,,,1936,210,214,Treats Descartes and Budan's rules,1,0,

,2,7,0,0,0,0,Sidi, A.,,,Unified treatment of regula falsi, Newton-Raphson, Secant and Steffensen methods for nonlinear equations,J. Online Math. Appl.,,,,2006,1,13,Title says it,1,0,

,18,0,0,0,0,0,Zcheb, E.,,,On the largest modulus of polynomial zeros,IEEE Trans. Circuits Systems,38,,,1991,333,337,Bounds,1,0,

,18,0,0,0,0,0,Zilovic, M. S.,Roytman, L. M,Combettes, P. L.,A bound for the zeros of polynomials,IEEE Trans. Circ. Sys. I. Fund. Theory Appl.,39 (6),,,1992,476,478,Bounds,1,0,

,21,0,0,0,0,0,Driver, K.,Jordaan, K.,,Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials,Numer. Math.,107 (4),,,2007,615,624,Interlacing of zeros of Laguene & Gegenbaur polynomials,1,0,

,21,0,0,0,0,0,Driver, K.,Jordaan, K.,Mbuyi, N.,Interlacing of the zeros of Jacobi polynomials with different parameters,Numer. Algorithms,49,,,2008,143,152,Title says it,1,0,

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,19,0,0,0,0,0,Cooke, R.,,,The history of mathematics: a brief course,,,Wiley & Sons,New York,1997,0,0,History of low degree equations,1,0,

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,2,13,0,0,0,0,Straffin, P.,,,Newton's method and fractal patterns,UMAP Journal,12.2,,,1991,143,164,Title says it,1,0,

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,19,0,0,0,0,0,Van Hee, L.,,,Li-Ye, mathematicien chinois du XIIIe siecle,T'oung Pao,14,,,1913,537,0,Quadratics,1,0,

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,19,0,0,0,0,0,Shih-chieh, C.,,,Thirteenth-century Chinese Mathematician,Dict. Sci. Biog.,3,,,1971,265,271,Used Homer's method,1,0,

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,29,0,0,0,0,0,Murthy, T. S. Bhanu.,,,A modern introduction to ancient Indian mathematics,,,Wiley Eastern,New Delhi,1992,0,0,Early surds,1,0,

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,19,0,0,0,0,0,Jha, P.,,,Aryabhata I and his contributions to mathematics,,,Bihar Research Society,Patna, India,1988,0,0,Hindu solution of quadratic,1,0,

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,9,0,0,0,0,0,Rice, J. R. (ed.),,,Mathematical software,,,Academic Press,New York,1971,0,0,Gives program for Jenkins-Traub method,1,0,

,10,11,0,0,0,0,Collins, G. E.,,,Infallible calculation of polynomial zeros, in "Mathematical Software III", ed J.R. Rice,,,Academic Press,New York,1977,35,68,Uses Sturm, interval methods,1,0,

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,25,0,0,0,0,0,Maser, H. (ed),,,Untersuchen über hörerer Arithmetik von Carl Friedrich Gauss,,,Chelsea,New York,1981,0,0,Existence,1,0,

,25,0,0,0,0,0,Neumann, O.,,,Die Entwicklung der Galois-Theorie zwischen Arithmetik und Topologie (1850 bis 1960),Arch. Hist. Exact Sci.,50,,,1997,291,329,,1,0,

,25,0,0,0,0,0,Sylow, L.,,,Les études d'Abel et ses découvertes, in "Niels Henrik Abel: Mémorial publié à l'occasion du centenaire de sa naissance Pt. 4",,,Gauthier-Villars,Paris,1902,1,59,Solution in radicals,1,0,

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,2,0,0,0,0,0,Carleson, L.,Gammelin, T.W.,,Complex Dynamics,,,Springer-Verlag,New York,1993,0,0,Brief mention of Newton's method,1,0,

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,17,0,0,0,0,0,Barrio, R.,Pena, J.M.,,Evaluation of the derivative of a polynomial in Bernstein form,Appl. Math. Comput.,167,,,2005,125,142,Title says it,1,0,

,17,0,0,0,0,0,Graillat, S.,Langlois, P.,Louvet, N.,Algorithms for accurate, validated, and fast polynomial evaluation,Japan J. Indust. Appl. Math.,26,,,2009,191,214,,1,0,

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,17,0,0,0,0,0,Barrio, R.,Pena, J.M.,,Basic conversions among univariate polynomial representations,C.R. Math.,339,,,2004,293,298,,1,0,

,19,0,0,0,0,0,Chasles, M.,,,Histoire de l'algebre,Comptes Rendus,13,,,1841,497,524,Early quadratics,1,0,

,13,0,0,0,0,0,Gandz, S.,,,On the origin of the word 'root',Amer. Math. Monthly,33,,,1926,261,265,Title says it,1,0,

,19,0,0,0,0,0,Datta, B. B.,Singh, A. N.,,History of Hindu Mathematics, Parts I and II,,,,,1935,0,0,Treats square & cube roots, quadratics,1,0,

,11,0,0,0,0,0,Jonckheere, E.,Ma, C.,,A further simplification to Jury's stability test,IEEE Trans. Circuits Syst.,36,,,1989,463,464,No note,1,0,

,7,0,0,0,0,0,Zheng, H.,Li, D.-S.,Liu, Y.-Z.,A new method of secant-like for nonlinear equations,Comm. in. Nonlinear Sci. Numer. Simul.,14,,,2009,2923,2927,order 2.618 with 2 evaluations,1,0,

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,19,0,0,0,0,0,Mayr, E,,,über die Auflosung algebraischer Gleichungssysteme durch hypergeometrische Functionen,Monatsch. Math. Phys.,45,,,1937,280,313,Analytic solution,1,0,

,2,0,0,0,0,0,Chabert, J. L.,,,Un demi-siecle de fractales: 1870-1920,Historia Mathematica,17,,,1990,339,365,Mentions Newton's method,1,0,

,19,0,0,0,0,0,Patterson, S. J.,,,Eisenstein and the Quintic Equation,Hist. Math.,17 (2),,,1990,132,141,Analytic solution of quintic,1,0,

,2,0,0,0,0,0,Neta, B.,,,On Popovski's method for nonlinear equations,Appl. Math. Comput.,201,,,2008,710,715,Gives a third order method with 3 evaluations,1,0,

,19,0,0,0,0,0,Karpinski, L. C.,,,Origines et Development de l' Algebre,Scientia,26,,,1919,89,101,Early quadratics,1,0,

,10,0,0,0,0,0,Pan, V. Y.,,,Numerical computation of a polynomial GCD and extensions,Information and Computation,167 (2),,,2001,71,85,Title says it,1,0,

,19,0,0,0,0,0,Bottazini, U.,,,Algebraische untersuchungen in italien 1850-1863,Hist. Math.,7 (1),,,1980,24,37,Treats quartic,1,0,

,21,0,0,0,0,0,Segura, J.,,,Reliable computation of the zeros of solutions of second order linear ODE's using a fourth order method,SIAM J. Numer. Anal.,48,,,2010,452,469,Treats Jacobi, Laguerre & Hermite polynomials etc,1,0,

,2,0,0,0,0,0,Cordero, A.,Hueso, J. L.,Martinez, E,A modified Newton-Jarratt composition,Numer. Algor.,55,,,2010,87,99,Sixth order with 4 evaluations,1,0,

,7,0,0,0,0,0,Yun, B. I.,,,Transformation methods for finding multiple roots of nonlinear equations,Appl. Math. Comput.,217,,,2010,599,606,Uses a Steffensen type method and a tanh transformation,1,0,

,28,0,0,0,0,0,Frayer, C.,Swenson, J. A.,,Polynomial root motion,Amer. Math. Monthly,117,,,2010,641,646,Considers motion of critical points as roots move,1,0,

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