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Iterative refinement for ill-conditioned linear systems
Publikationstyp
Journal Article
Date Issued
2009-10
Sprache
English
Author(s)
Institut
TORE-URI
Volume
26
Issue
2/3
Start Page
465
End Page
476
Citation
Japan Journal of Industrial and Applied Mathematics 2/3 (26): 465-476 (2009)
Publisher DOI
Scopus ID
Publisher
Springer Nature
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.
Subjects
Ill-conditioned linear systems
Iterative refinement
Verified numerical computation
DDC Class
004: Informatik
510: Mathematik
More Funding Information
The authors are supported by the Grant-in-Aid for Specially Promoted Research from the MEXT, Japan: "Establishment of Verified Numerical Computation" (No. 17002012).