Improved algorithms for computing determinants and resultants

[1]  R. Graham,et al.  A Hadamard-Type Bound on the Coefficients of a Determinant of Polynomials , 1973 .

[2]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[3]  O. Lossers.  A Hadamard-Type Bound on the Coefficients of a Determinant of Polynomials (A. J. Goldstein and R. L. Graham) , 1974 .

[4]  David Y. Y. Yun,et al.  On square-free decomposition algorithms , 1976, SYMSAC '76.

[5]  David Y. Y. Yun,et al.  Fast Solution of Toeplitz Systems of Equations and Computation of Padé Approximants , 1980, J. Algorithms.

[6]  G. E. Collins,et al.  Real Zeros of Polynomials , 1983 .

[7]  Richard E. Ewing,et al.  "The Merging of Disciplines: New Directions in Pure, Applied, and Computational Mathematics" , 1986 .

[8]  Douglas H. Wiedemann.  Solving sparse linear equations over finite fields , 1986, IEEE Trans. Inf. Theory.

[9]  S. Smale.  Newton’s Method Estimates from Data at One Point , 1986 .

[10]  Erich Kaltofen,et al.  Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[11]  John F. Canny,et al.  Some algebraic and geometric computations in PSPACE , 1988, STOC '88.

[12]  Myong-Hi Kim.  On approximate zeros and rootfinding algorithms for a complex polynomial , 1988 .

[13]  Erich Kaltofen,et al.  Solving systems of nonlinear polynomial equations faster , 1989, ISSAC '89.

[14]  Erich Kaltofen,et al.  Computing with Polynomials Given By Black Boxes for Their Evaluations: Greatest Common Divisors, Factorization, Separation of Numerators and Denominators , 1990, J. Symb. Comput..

[15]  John F. Canny,et al.  Generalised Characteristic Polynomials , 1990, J. Symb. Comput..

[16]  Erich Kaltofen,et al.  On Wiedemann's Method of Solving Sparse Linear Systems , 1991, AAECC.

[17]  Victor Y. Pan,et al.  Processor efficient parallel solution of linear systems over an abstract field , 1991, SPAA '91.

[18]  V. Pan.  PARAMETRIZATION OF NEWTON'S ITERATION FOR COMPUTATIONS WITH STRUCTURED MATRICES AND APPLICATIONS , 1992 .

[19]  Dinesh Manocha,et al.  Implicit Representation of Rational Parametric Surfaces , 1992, J. Symb. Comput..

[20]  Richard Zippel,et al.  Effective polynomial computation , 1993, The Kluwer international series in engineering and computer science.

[21]  J. McNamee.  A bibliography on roots of polynomials , 1993 .

[22]  Dinesh Manocha,et al.  Efficient Algorithms for MultiPolynomial Resultant , 1993, Comput. J..

[23]  Dinesh Manocha,et al.  Multipolynomial Resultant Algorithms , 1993, J. Symb. Comput..

[24]  D. Coppersmith.  Solving homogeneous linear equations over GF (2) via block Wiedemann algorithm , 1994 .

[25]  W. Deren,et al.  The theory of Smale's point estimation and its applications , 1995 .

[26]  Eecient Incremental Algorithms for the Sparse Resultant and the Mixed Volume , 1995 .

[27]  Michael Clausen,et al.  Algebraic complexity theory , 1997, Grundlehren der mathematischen Wissenschaften.

[28]  Victor Y. Pan,et al.  Solving a Polynomial Equation: Some History and Recent Progress , 1997, SIAM Rev..

[29]  J. McNamee.  A supplementary bibliography On roots of polynomials , 1997 .

[30]  F. Rouillier.  Solving Zero-dimensional Polynomial Systems through the Rational Univariate Representation , 1998 .

[31]  Joachim von zur Gathen,et al.  Modern Computer Algebra , 1998 .

[32]  Ioannis Z. Emiris,et al.  A Complete Implementation for Computing General Dimensional Convex Hulls , 1998, Int. J. Comput. Geom. Appl..

[33]  Bernard Mourrain,et al.  Computing the Isolated Roots by Matrix Methods , 1998, J. Symb. Comput..

[34]  Victor Y. Pan,et al.  Sign Determination in Residue Number Systems , 1999, Theor. Comput. Sci..

[35]  Manuel Bronstein,et al.  Fast deterministic computation of determinants of dense matrices , 1999, ISSAC '99.

[36]  Fabrice Rouillier,et al.  Solving Zero-Dimensional Systems Through the Rational Univariate Representation , 1999, Applicable Algebra in Engineering, Communication and Computing.

[37]  Gilles Villard,et al.  On computing the determinant and Smith form of an integer matrix , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[38]  John F. Canny,et al.  A subdivision-based algorithm for the sparse resultant , 2000, JACM.

[39]  Victor Y. Pan,et al.  Certification of Numerical Computation of the Sign of the Determinant of a Matrix , 2001, Algorithmica.

[40]  C. D'Andrea.  Macaulay style formulas for sparse resultants , 2001 .

[41]  Steven Fortune,et al.  Polynomial root finding using iterated Eigenvalue computation , 2001, ISSAC '01.

[42]  V. Pan.  Structured Matrices and Polynomials: Unified Superfast Algorithms , 2001 .

[43]  Erich Kaltofen.  An output-sensitive variant of the baby steps/giant steps determinant algorithm , 2002, ISSAC '02.

[44]  Victor Y. Pan,et al.  TR-2002019: Improved Algorithms for Computing Determinants and Resultants , 2002 .

[45]  Victor Y. Pan,et al.  Univariate Polynomials: Nearly Optimal Algorithms for Numerical Factorization and Root-finding , 2002, J. Symb. Comput..

[46]  R. Gregory Taylor,et al.  Modern computer algebra , 2002, SIGA.

[47]  Victor Y. Pan.  Randomized Acceleration of Fundamental Matrix Computations , 2002, STACS.

[48]  Victor Y. Pan,et al.  Symbolic and Numeric Methods for Exploiting Structure in Constructing Resultant Matrices , 2002, J. Symb. Comput..

[49]  Zhonggang Zeng.  A method computing multiple roots of inexact polynomials , 2003, ISSAC '03.

[50]  Slobodan Ilic,et al.  The guaranteed convergence of Laguerre-like method , 2003 .

[51]  Arne Storjohann,et al.  High-order lifting and integrality certification , 2003, J. Symb. Comput..

[52]  Erich Kaltofen,et al.  On the complexity of computing determinants , 2001, computational complexity.

[53]  P. Zimmermann,et al.  Efficient isolation of polynomial's real roots , 2004 .

[54]  Manindra Agrawal,et al.  PRIMES is in P , 2004 .

[55]  Miodrag S. Petkovic,et al.  Safe convergence of simultaneous methods for polynomial zeros , 2004, Numerical Algorithms.

[56]  V. Pan,et al.  TR-2004013: Toeplitz and Hankel Meet Hensel and Newton: Nearly Optimal Algorithms and Their Practical Acceleration with Saturated Initialization , 2004 .

[57]  Arne Storjohann,et al.  The shifted number system for fast linear algebra on integer matrices , 2005, J. Complex..

[58]  Dario Bini,et al.  Numerical computation of polynomial zeros by means of Aberth's method , 1996, Numerical Algorithms.

[59]  M. Petkovic,et al.  Point estimation of simultaneous methods for solving polynomial equations , 2007 .