日本応用数理学会論文誌
Online ISSN : 2424-0982
ISSN-L : 0917-2246
LanczosプロセスのリスタートによるCGS法の安定化(<特集>行列・固有値問題における線形計算アルゴリズムとその応用)
多田野 寛人櫻井 鉄也
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2005 年 15 巻 2 号 p. 129-143

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抄録
The Conjugate Gradient Squared (CGS) method has been proposed for solving linear systems with non-Hermitian matrix. This method is known to be unstable because the residual often increases rapidly due to near-breakdown. In this paper, we analyze two causes of near-breakdown in the CGS method and derive a condition of detecting it. Moreover, we propose a method for avoiding near-breakdown in the CGS method by restarting Lanczos process. Effects of the CGS method with restart have been illustrated by some numerical experiments.
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© 2005 一般社団法人 日本応用数理学会
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