A note on the preconditioner Pm = (I + Sm)

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:225

Letter

Kohno, Toshiyuki¹  Niki, Hiroshi¹ 

[1] Okayama Univ Sci, Fac Informat, Okayama, Japan

关键词: Preconditioner;    Iterative method;    Linear system;   

DOI  :  10.1016/j.cam.2008.07.042

来源: Elsevier

【 摘 要 】

Kotakemori et al. [H. Kotakemori, K. Harada, M. Morimoto, H. Niki. A comparison theorem for the iterative method with the preconditioner (I + S-max), Journal of Computational and Applied Mathematics 145 (2002) 373-378] have reported that the convergence rate of the iterative method with a preconditioner P-m = (I + S) Was Superior to one of the modified Gauss-Seidel method under the condition. These authors derived a theorem comparing the Gauss-Seidel method with the proposed method. However, through application of a counter example, Wen Li [Wen Li, A note on the preconditioned GaussSeidel (GS) method for linear systems, journal of Computational and Applied Mathematics 182 (2005) 81-91] pointed Out that there exists a special matrix that does not satisfy this comparison theorem. In this note, we analyze the reason why such a to Counter example may be produced, and propose a preconditioner to overcome this problem. (C) 2009 Published by Elsevier B.V.

【 授权许可】

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