# ON CONVERGENCE OF THE MODIFIED GAUSS-SEIDEL ITERATIVE METHOD FOR H-MATRIX LINEAR SYSTEM

• Miao, Shu-Xin (School of Mathematics and Statistics Lanzhou University, Department of Mathematics Northwest Normal University) ;
• Zheng, Bing (School of Mathematics and Statistics Lanzhou University)
• Published : 2013.07.31

#### Abstract

In 2009, Zheng and Miao [B. Zheng and S.-X. Miao, Two new modified Gauss-Seidel methods for linear system with M-matrices, J. Comput. Appl. Math. 233 (2009), 922-930] considered the modified Gauss-Seidel method for solving M-matrix linear system with the preconditioner $P_{max}$. In this paper, we consider the modified Gauss-Seidel method for solving the linear system with the generalized preconditioner $P_{max}({\alpha})$, and study its convergent properties when the coefficient matrix is an H-matrix. Numerical experiments are performed with different examples, and the numerical results verify our theoretical analysis.

#### Acknowledgement

Supported by : National Natural Science Foundation of China

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