Root-Refining for a Polynomial Equation
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[1] Victor Y. Pan,et al. Univariate polynomials: nearly optimal algorithms for factorization and rootfinding , 2001, ISSAC '01.
[2] V. Pan. The amended DSeSC power method for polynomial root-finding , 2005 .
[3] V. Pan,et al. Polynomial and Matrix Computations , 1994, Progress in Theoretical Computer Science.
[4] Victor Y. Pan,et al. Univariate Polynomials: Nearly Optimal Algorithms for Numerical Factorization and Root-finding , 2002, J. Symb. Comput..
[5] James H. Curry,et al. On zero finding methods of higher order from data at one point , 1989, J. Complex..
[6] Béla Bollobás,et al. A small probabilistic universal set of starting points for finding roots of complex polynomials by Newton's method , 2010, Math. Comput..
[7] K. Mahler. An inequality for the discriminant of a polynomial. , 1964 .
[8] Victor Y. Pan,et al. Solving a Polynomial Equation: Some History and Recent Progress , 1997, SIAM Rev..
[9] Louis W. Ehrlich,et al. A modified Newton method for polynomials , 1967, CACM.
[10] Victor Y. Pan. Solving Polynomials with Computers , 1998 .
[11] A. Ostrowski. Solution of equations and systems of equations , 1967 .
[12] Victor Y. Pan,et al. New progress in real and complex polynomial root-finding , 2011, Comput. Math. Appl..
[13] Immo O. Kerner,et al. Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen , 1966 .
[14] Alexandre Ostrowski. Recherches sur la méthode de graeffe et les zéros des polynomes et des séries de laurent , 1940 .
[15] Oliver Aberth,et al. Iteration methods for finding all zeros of a polynomial simultaneously , 1973 .
[16] A. Householder. Dandelin, Lobacevskii, or Graeffe , 1959 .
[17] M. Petkovic,et al. Point estimation of simultaneous methods for solving polynomial equations , 2007 .
[18] Victor Y. Pan,et al. Multivariate Polynomials, Duality, and Structured Matrices , 2000, J. Complex..
[19] Peter Kirrinnis,et al. Partial Fraction Decomposition in (z) and Simultaneous Newton Iteration for Factorization in C[z] , 1998, J. Complex..
[20] Gwilym M. Jenkins,et al. Time series analysis, forecasting and control , 1972 .
[21] B. Wyman,et al. Linear algebra for control theory , 1994 .
[22] S. Smale. Newton’s Method Estimates from Data at One Point , 1986 .
[23] John H. Reif,et al. An O(n/sup 1+/spl epsiv// log b) algorithm for the complex roots problem , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.
[24] E. Bell. The development of mathematics , 1941 .
[25] Myong-Hi Kim. Computation complexity of the euler algorithms for the roots of complex polynomials , 1986 .
[26] A. C. Aitken. XXV.—On Bernoulli's Numerical Solution of Algebraic Equations , 1927 .
[27] Jean Charles Faugère,et al. A new efficient algorithm for computing Gröbner bases without reduction to zero (F5) , 2002, ISSAC '02.
[28] S. Smale. The fundamental theorem of algebra and complexity theory , 1981 .
[29] V. Pan. Optimal and nearly optimal algorithms for approximating polynomial zeros , 1996 .
[30] D. E. Muller. A method for solving algebraic equations using an automatic computer , 1956 .
[31] Victor Y. Pan,et al. Efficient polynomial root-refiners: A survey and new record efficiency estimates , 2012, Comput. Math. Appl..
[32] Victor Y. Pan,et al. Numerical methods for roots of polynomials , 2007 .
[33] James Renegar,et al. On the worst-case arithmetic complexity of approximating zeros of polynomials , 1987, J. Complex..
[34] Clifford T. Mullis,et al. A Newton-Raphson method for moving-average spectral factorization using the Euclid algorithm , 1990, IEEE Trans. Acoust. Speech Signal Process..
[35] S. Barnett. Polynomials and linear control systems , 1983 .
[36] K. Weierstrass. Neuer Beweis des Fundamentalsatzes der Algebra , 2013 .
[37] J. McNamee. A 2002 update of the supplementary bibliography on roots of polynomials , 2002 .
[38] Carl B. Boyer,et al. A History of Mathematics. , 1993 .
[39] G. Wilson. Factorization of the Covariance Generating Function of a Pure Moving Average Process , 1969 .
[40] Victor Y. Pan,et al. Root-finding by expansion with independent constraints , 2011, Comput. Math. Appl..
[41] P. Dooren. Some numerical challenges in control theory , 1994 .
[42] Victor Y. Pan,et al. Optimal (up to polylog factors) sequential and parallel algorithms for approximating complex polynomial zeros , 1995, STOC '95.