Iterative refinement for ill-conditioned linear systems

Shin'ichi Oishi, Takeshi Ogita, Siegfried M. Rump

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper treats a linear equation Aυ = b, where A ∈ F n×n and b ∈ Fn. Here, F is a set of floating point numbers. Let u be the unit round-off of the working precision and κ(A) = ∥A∥∞∥A-1∥∞ be the condition number of the problem. In this paper, ill-conditioned problems with 1 < uκ(A) < ∞ are considered and an iterative refinement algorithm for the problems is proposed. In this paper, the forward and backward stability will be shown for this iterative refinement algorithm.

Original languageEnglish
Pages (from-to)465-476
Number of pages12
JournalJapan Journal of Industrial and Applied Mathematics
Volume26
Issue number2-3
DOIs
Publication statusPublished - 2009 Oct

Keywords

  • Ill-conditioned linear systems
  • Iterative refinement
  • Verified numerical computation

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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