Summary

International Symposium on Nonlinear Theory and its Applications

2008

Session Number:C2L-C

Session:

Number:C2L-C5

Iterative Refinement for Ill-conditioned Linear Equations.

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

pp.-

Publication Date:2008/9/7

Online ISSN:2188-5079

DOI:10.34385/proc.42.C2L-C5

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This paper treats a linear equation
Av = b, where A ∈ Fn×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.