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Pseudofactors of multivariate polynomials

Authors:

Hans J. Stetter,

Lihong ZhiAuthors Info & Claims

ISSAC '00: Proceedings of the 2000 international symposium on Symbolic and algebraic computation

Pages 161 - 168

https://doi.org/10.1145/345542.345616

Published: 01 July 2000 Publication History

Abstract

We treat pseudo-factorization of a multivariate polynomial p over C as an overdetermined bilinear system for the coefficients of the factors. If the specified data (coefficients of p) are sufficiently close to the manifold of consistent data we project onto it by solving a well-chosen subsystem (otherwise we quit). On the manifold, we reduce the backward error by a linearized minimization procedure. The resulting algorithm appears to extend the range of treatable cases - in terms of number of variables and total degree - considerably.

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Cited By

Wu WZeng Z(2015)The Numerical Factorization of PolynomialsFoundations of Computational Mathematics10.1007/s10208-015-9289-117:1(259-286)Online publication date: 19-Nov-2015
https://doi.org/10.1007/s10208-015-9289-1
Feng YWu WZhang JChen J(2014)Exact bivariate polynomial factorization over ℚ by approximation of rootsJournal of Systems Science and Complexity10.1007/s11424-014-2170-528:1(243-260)Online publication date: 28-Aug-2014
https://doi.org/10.1007/s11424-014-2170-5
Leykin AVerschelde J(2009)Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithmInternational Journal of Computational Science and Engineering10.1504/IJCSE.2009.0270014:2(94-101)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.1504/IJCSE.2009.027001
Show More Cited By

Index Terms

Pseudofactors of multivariate polynomials
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Algebraic algorithms
2. Mathematics of computing
  1. Mathematical analysis
    1. Nonlinear equations
    2. Numerical analysis
      1. Computations on polynomials
      2. Number-theoretic computations

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cover image ACM Conferences

ISSAC '00: Proceedings of the 2000 international symposium on Symbolic and algebraic computation

July 2000

309 pages

ISBN:1581132182

DOI:10.1145/345542

Editor:
Carlo Traverso
Univ. di Pisa

Copyright © 2000 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 July 2000

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ISSAC '00 Paper Acceptance Rate 40 of 98 submissions, 41%;

Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

Wu WZeng Z(2015)The Numerical Factorization of PolynomialsFoundations of Computational Mathematics10.1007/s10208-015-9289-117:1(259-286)Online publication date: 19-Nov-2015
https://doi.org/10.1007/s10208-015-9289-1
Feng YWu WZhang JChen J(2014)Exact bivariate polynomial factorization over ℚ by approximation of rootsJournal of Systems Science and Complexity10.1007/s11424-014-2170-528:1(243-260)Online publication date: 28-Aug-2014
https://doi.org/10.1007/s11424-014-2170-5
Leykin AVerschelde J(2009)Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithmInternational Journal of Computational Science and Engineering10.1504/IJCSE.2009.0270014:2(94-101)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.1504/IJCSE.2009.027001
Sasaki TOokura YSasaki TShirayanagi KKotsireas I(2009)Approximate factorization of polynomials over ZProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577216(169-176)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1577190.1577216
Qin XFeng YChen JZhang JSasaki TShirayanagi KKotsireas I(2009)Finding exact minimal polynomial by approximationsProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577211(125-132)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1577190.1577211
Cuyt ALee WSasaki TShirayanagi KKotsireas I(2009)Extracting numerical factors of multivariate polynomials from taylor expansionsProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577201(35-44)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1577190.1577201
Sekigawa H(2009)On real factors of real interval polynomialsJournal of Symbolic Computation10.1016/j.jsc.2008.04.01444:7(908-922)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.1016/j.jsc.2008.04.014
Zeng Z(2009)Regularization and Matrix Computation in Numerical Polynomial AlgebraApproximate Commutative Algebra10.1007/978-3-211-99314-9_5(125-162)Online publication date: 21-Aug-2009
https://doi.org/10.1007/978-3-211-99314-9_5
Sekigawa HWang D(2007)On real factors of real interval polynomialsProceedings of the 2007 international symposium on Symbolic and algebraic computation10.1145/1277548.1277593(331-338)Online publication date: 29-Jul-2007
https://dl.acm.org/doi/10.1145/1277548.1277593
Galligo Avan Hoeij MWatt SVerschelde J(2007)Approximate bivariate factorizationProceedings of the 2007 international workshop on Symbolic-numeric computation10.1145/1277500.1277502(1-10)Online publication date: 25-Jul-2007
https://dl.acm.org/doi/10.1145/1277500.1277502
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