1. Modified SOR-like method for the augmented system.
- Author
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Shao, Xinhui, Li, Zheng, and Li, Changjun
- Subjects
METHOD of steepest descent (Numerical analysis) ,ITERATIVE methods (Mathematics) ,MATRICES (Mathematics) ,LINEAR systems ,NUMERICAL analysis ,COMPUTATIONAL mathematics - Abstract
The SOR-like method with two real parameters ω and α is considered for solving the augmented system. The new method is called the modified SOR-like method (MSOR-like method). The MSOR-like method becomes the SOR-like method when α = 0. The functional equation relating the parameters and eigenvalues of the iteration matrix of the MSOR-like method is obtained. Hence the necessary and sufficient condition for the convergence of the GSOR-like method is derived. It is shown that when α is negative, the convergence domain for the parameter ω for the MSOR-like method is larger than that for the SOR-like method. Finally, a numerical computation based on a particular linear system is given which clearly shows that the MSOR-like method outperforms the SOR-like method. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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