Complete numerical isolation of real roots in zero-dimensional triangular systems

Jin San Cheng, Xiao Shan Gao, Chee Yap

Research output: Contribution to journalArticle

Abstract

We present a complete numerical algorithm for isolating all the real zeros of a zero-dimensional triangular polynomial system Fn ⊆ Z [x1 ... xn]. Our system Fn is general, with no further assumptions. In particular, our algorithm successfully treats multiple zeros directly in such systems. A key idea is to introduce evaluation bounds and sleeve bounds. We also present a much more efficient algorithm for zero-dimensional triangular systems without multiple roots. We implemented our algorithms, and promising experimental results are shown.

Original languageEnglish (US)
Pages (from-to)768-785
Number of pages18
JournalJournal of Symbolic Computation
Volume44
Issue number7
DOIs
StatePublished - Jul 2009

Fingerprint

Triangular Systems
Real Roots
Zero-dimensional
Isolation
Multiple Zeros
Multiple Roots
Polynomial Systems
Numerical Algorithms
Efficient Algorithms
Evaluation
Zero
Experimental Results
Polynomials

Keywords

  • Evaluation bound
  • Real zero isolation
  • Sleeve bound
  • Triangular system

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

Cite this

Complete numerical isolation of real roots in zero-dimensional triangular systems. / Cheng, Jin San; Gao, Xiao Shan; Yap, Chee.

In: Journal of Symbolic Computation, Vol. 44, No. 7, 07.2009, p. 768-785.

Research output: Contribution to journalArticle

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