Iterative refinement for ill-conditioned linear systems

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

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)465-476
ページ数12
ジャーナルJapan Journal of Industrial and Applied Mathematics
26
2-3
DOI
出版ステータスPublished - 2009 10

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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