On convergence of the modified Gauss-Seidel iterative method for H-matrix linear system
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In 2009, Zheng and Miao [B. Zheng and S.-X. Miao, Twonew modified Gauss-Seidel methods for linear system with M-matrices,J. Comput. Appl. Math. 233 (2009), 922–930] considered the modifiedGauss-Seidel method for solving M-matrix linear system with the pre-conditioner Pmax. In this paper, we consider the modified Gauss-Seidelmethod for solving the linear system with the generalized preconditionerPmax(a), and study its convergent properties when the coefficient ma-trix is an H-matrix. Numerical experiments are performed with differentexamples, and the numerical results verify our theoretical analysis.
Abstract
In 2009, Zheng and Miao [B. Zheng and S.-X. Miao, Twonew modified Gauss-Seidel methods for linear system with M-matrices,J. Comput. Appl. Math. 233 (2009), 922–930] considered the modifiedGauss-Seidel method for solving M-matrix linear system with the pre-conditioner Pmax. In this paper, we consider the modified Gauss-Seidelmethod for solving the linear system with the generalized preconditionerPmax(a), and study its convergent properties when the coefficient ma-trix is an H-matrix. Numerical experiments are performed with differentexamples, and the numerical results verify our theoretical analysis.
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