Preconditioned Gauss-Seidel iterative method for $Z$-matrices linear systems
Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 303-314
https://doi.org/10.4134/BKMS.2011.48.2.303
Printed March 1, 2011
Hailong Shen, Xinhui Shao, Zhenxing Huang, and Chunji Li
Northeastern University, Northeastern University, Northeastern University, Northeastern University
Abstract : For $Ax=b$, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type $P=I+S\left( \alpha \right) $ to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses $P=I+S\left( \alpha \right) +\bar{K}\left( \beta \right) $ as a preconditioner. We present some comparison theorems, which show the rate of convergence of the new method is faster than the basic method and the method in [7] theoretically. Numerical examples show the effectiveness of our algorithm.
Keywords : Gauss-Seidel iterative method, preconditioned method, $Z$-matrix, diagonal dominant matrix
MSC numbers : 65F08
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