Finding all real zeros of polynomial systems using multi-resultant

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5 Citations (Scopus)

Abstract

We present a new practicable method for approximating all real zeros of polynomial systems using the resultants method. It is based on the theory of multi-resultants. We build a sparse linear system. Then, we solve it by the quasi-minimal residual method. Once our test function changes its sign, we apply the secant method to approximate the root. The unstable calculation of the determinant of the large sparse matrix is replaced by solving a sparse linear system. This technique will be able to take advantage of the sparseness of the resultant matrix. Theoretical and numerical results are presented.

Original languageEnglish
Pages (from-to)417-428
Number of pages12
JournalJournal of Computational and Applied Mathematics
Volume167
Issue number2
DOIs
Publication statusPublished - Jun 1 2004

Keywords

  • Continuation method
  • Real zeros
  • Resultant matrix
  • Secant method
  • Test function

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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