Iterative refinement for ill-conditioned linear systems

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Issue number2-3
Publication statusPublished - 2009 Oct


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

ASJC Scopus subject areas

  • General Engineering
  • Applied Mathematics


Dive into the research topics of 'Iterative refinement for ill-conditioned linear systems'. Together they form a unique fingerprint.

Cite this