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

Jin San Cheng, Xiao Shan Gao, Chee Keng Yap

Research output: Contribution to journalArticlepeer-review


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
Issue number7
StatePublished - Jul 2009


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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics

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