Iterative refinement for ill-conditioned linear systems

Shinichi 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
    Publication statusPublished - 2009 Oct

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    Keywords

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

    ASJC Scopus subject areas

    • Applied Mathematics
    • Engineering(all)

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