DOI QR코드

DOI QR Code

PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR Z-MATRICES LINEAR SYSTEMS

Shen, Hailong;Shao, Xinhui;Huang, Zhenxing;Li, Chunji

  • Received : 2009.06.26
  • Published : 2011.03.31

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 (${\alpha}$) 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 (${\alpha}$) + $\bar{K}({\beta})$ 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

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Acknowledgement

Supported by : National Natural Science Foundation of China, Central Universities