Constructive root bound for k-ary rational input numbers

Sylvain Pion, Chee K. Yap

Research output: Contribution to journalArticle

Abstract

Guaranteeing accuracy is the critical capability in exact geometric computation, an important paradigm for constructing robust geometric algorithms. Constructive root bounds is the fundamental technique needed to achieve such guaranteed accuracy. Current bounds are overly pessimistic in the presence of general rational input numbers. In this paper, we introduce a method which greatly improves the known bounds for k-ary rational input numbers. Since a majority of input numbers in scientific and engineering applications are either binary (k = 2) or decimal (k = 10), our results could lead to a significant speedup for a large class of applications. We apply our method to two of the best available constructive root bounds, the BFMSS Bound and the Degree-Measure Bound. Implementation and experimental results based on the Core Library are reported.

Original languageEnglish (US)
Pages (from-to)361-376
Number of pages16
JournalTheoretical Computer Science
Volume369
Issue number1-3
DOIs
StatePublished - Dec 15 2006

Keywords

  • Constructive root bounds
  • Exact geometric computation
  • Robust numerical algorithms
  • k-Ary rational numbers

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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