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

Jin San Cheng, Xiao Shan Gao, Chee Keng Yap

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present a complete numerical algorithm of 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 treat multiple zeros directly in such systems. A key idea is to introduce evaluation bounds and sleeve bounds. We implemented our algorithm and promising experimental results are shown.

Original languageEnglish (US)
Title of host publicationISSAC 2007 - Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation
Pages92-99
Number of pages8
DOIs
StatePublished - 2007
EventISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation - London, ON, Canada
Duration: Jul 29 2007Aug 1 2007

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Other

OtherISSAC 2007 - 2007 International Symposium on Symbolic and Algebraic Computation
CountryCanada
CityLondon, ON
Period7/29/078/1/07

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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