Tight enclosures of solutions of linear systems

Takeshi Ogita, Shin’ichi Oishi

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)


This paper is concerned with the problem of verifying the accuracy of an approximate solution of a linear system. A fast method of calculating both lower and upper error bounds of the approximate solution is proposed. By the proposed method, it is possible to obtain the error bounds which are as tight as needed. As a result, it can be verified that the obtained error bounds are of high quality. Numerical results are presented elucidating properties and efficiencies of the proposed verification method.

Original languageEnglish
Title of host publicationInternational Series of Numerical Mathematics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
Publication statusPublished - 2009

Publication series

NameInternational Series of Numerical Mathematics
ISSN (Print)0373-3149
ISSN (Electronic)2296-6072


  • Linear system
  • Tight enclosure
  • Verified numerical computation

ASJC Scopus subject areas

  • Numerical Analysis
  • Control and Optimization
  • Applied Mathematics


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