TY - JOUR
T1 - Iterative refinement for ill-conditioned linear systems
AU - Oishi, Shin'ichi
AU - Ogita, Takeshi
AU - Rump, Siegfried M.
PY - 2009/10
Y1 - 2009/10
N2 - 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.
AB - 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.
KW - Ill-conditioned linear systems
KW - Iterative refinement
KW - Verified numerical computation
UR - http://www.scopus.com/inward/record.url?scp=77149123329&partnerID=8YFLogxK
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U2 - 10.1007/BF03186544
DO - 10.1007/BF03186544
M3 - Article
AN - SCOPUS:77149123329
SN - 0916-7005
VL - 26
SP - 465
EP - 476
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
IS - 2-3
ER -