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A note on the preconditioner

✍ Scribed by Toshiyuki Kohno; Hiroshi Niki

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
334 KB
Volume
225
Category
Article
ISSN
0377-0427

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✦ Synopsis

have reported that the convergence rate of the iterative method with a preconditioner P m = (I + S m ) 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.

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