Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 901–912
Abstract
The generalized successive overrelaxation (GSOR) method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102(2005), pp.1-38] for solving the augmented system of linear equations, and the optimal iteration parameters and the corresponding optimal convergence factor were exactly obtained. In this paper, we further estimate the contraction and the semi-contraction factors of the GSOR method. The motivation of the study is that the convergence speed of an iteration method is actually decided by the contraction factor but not by the spectral radius in finite-step iteration computations. For the nonsingular augmented linear system, under some restrictions we obtain the contraction domain of the parameters involved, which guarantees that the contraction factor of the GSOR method is less than one. For the singular but consistent augmented linear system, we also obtain the semi-contraction domain of the parameters in a similar fashion. Finally, we use two numerical examples to verify the theoretical results and the effectiveness of the GSOR method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1004-m3180
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 901–912
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Contraction and semi-contraction factors Augmented linear system GSOR method Convergence.
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