Reducing exact computations to obtain exact results based on stabilization techniques

Kiyoshi Shirayanagi, Hiroshi Sekigawa

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

4 Citations (Scopus)

Abstract

For a certain class of algebraic algorithms, we propose a new method that reduces the number of exact computational steps needed for obtaining exact results. This method is the floating-point interval method using zero rewriting and symbols. Zero rewriting, which is from stabilization techniques, rewrites an interval coefficient into the zero interval if the interval contains zero. Symbols are used to keep track of the execution path of the original algorithm with exact computations, so that the associated real coefficients can be computed by evaluating the symbols. The key point is that at each stage of zero rewriting, one checks to see if the zero rewriting is really correct; namely, an interval that has been rewritten into zero is really zero by exploiting the associated symbol. This method mostly uses floating-point computations; the exact computations are only performed at the stage of zero rewriting and in the final evaluation to get the exact coefficients. Moreover, one does not need to check the correctness of the output.

Original languageEnglish
Title of host publicationProceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009
Pages191-197
Number of pages7
Publication statusPublished - 1 Dec 2009
Event2009 Conference on Symbolic Numeric Computation, SNC 2009 - Kyoto, Japan
Duration: 3 Aug 20095 Aug 2009

Publication series

NameProceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009

Conference

Conference2009 Conference on Symbolic Numeric Computation, SNC 2009
CountryJapan
CityKyoto
Period3/08/095/08/09

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Keywords

  • Exact results
  • Floating-point computation
  • Interval arithmetic
  • Log
  • Stabilization techniques
  • Zero rewriting

Cite this

Shirayanagi, K., & Sekigawa, H. (2009). Reducing exact computations to obtain exact results based on stabilization techniques. In Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009 (pp. 191-197). (Proceedings of the 2009 Conference on Symbolic Numeric Computation, SNC 2009).