Computation of sharp rigorous componentwise error bounds for the approximate solutions of systems of linear equations

Takeshi Ogita, Shin'ichi Oishi, Yasunori Ushiro

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

This paper is concerned with the problem of verifying the accuracy of approximate solutions of systems of linear equations. Recently, fast algorithms for calculating guaranteed error bounds of computed solutions of system's of linear equations have been proposed using the rounding mode controlled verification method and the residual iterative verification method. In this paper, a new verification method for systems of linear equations is proposed. Using this verification method, componentwise verified error bounds of approximate solutions of systems of linear equations can be calculated. Numerical results are presented to illustrate that it is possible to get very sharp error bounds of computed solutions of systems of linear equations whose coefficient matrices are symmetric and positive definite.

Original languageEnglish
Pages (from-to)229-239
Number of pages11
JournalReliable Computing
Volume9
Issue number3
DOIs
Publication statusPublished - 2003 Jun 1

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

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