Simultaneous factorization of a polynomial by rational approximation

Carsten Carstensen, Tetsuya Sakurai

Research output: Contribution to journalArticle

Abstract

In this note we present a numerical method to approximate some relatively prime factors of a polynomial simultaneously. Our approach gives methods of arbitrary order; Grau's method (Carstensen, 1992; Grau, 1971) is obtained as the second order method which is Durand-Kerner's method when we have linear factors. For linear factors our approach yields the simultaneous methods introduced in Sakurai et al. (1991). We prove local convergence and estimate the R-order of the total step version as well as the single step version of the methods. We derive an algorithm and present numerical examples which confirm the convergence behavior theoretically predicted. © 1995.

Original languageEnglish
Pages (from-to)165-178
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume61
Issue number2
Publication statusPublished - 31 Jul 1995

Keywords

  • Factorization of polynomials
  • Polynomial zeros
  • Rational approximation
  • Simultaneous methods
  • Single step methods

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