Fast verified solutions of linear systems

Takeshi Ogita*, Shin'ichi Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear system. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.

Original languageEnglish
Pages (from-to)169-190
Number of pages22
JournalJapan Journal of Industrial and Applied Mathematics
Issue number2-3
Publication statusPublished - 2009 Oct


  • Self-validating methods
  • Verified numerical computation
  • Verified solutions of linear systems

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics


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