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PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR Z-MATRICES LINEAR SYSTEMS
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 Title & Authors
PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR Z-MATRICES LINEAR SYSTEMS
Shen, Hailong; Shao, Xinhui; Huang, Zhenxing; Li, Chunji;
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 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 () 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 () + 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;
 Language
English
 Cited by
 References
1.
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994.

2.
A. D. Gunawardena, S. K. Jain, and L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154/156 (1991), 123-143. crossref(new window)

3.
A. Hadjidimos, D. Noutsos, and M. Tzoumas, More on modifications and improvements of classical iterative schemes for M-matrices, Linear Algebra Appl. 364 (2003), 253-279. crossref(new window)

4.
J. Hu, The iterative methods of the linear equations, Beijing: Science Press (1997), 63-64.

5.
T. Kohno, H. Kotakemori, H. Niki, and M. Usui, Improving the modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997), 113-123. crossref(new window)

6.
H. Kotakemori, H. Niki, and N. Okamoto, Accelerated iterative method for Z-matrices, J. Comput. Appl. Math. 75 (1996), no. 1, 87-97. crossref(new window)

7.
J. Li and T. Huang, Preconditioning methods for Z-matrices, Acta Math. Sci. Ser. A Chin. Ed. 25 (2005), no. 1, 5-10.

8.
J. P. Milaszewicz, Improving Jacobi and Gauss-Seidel iterations, Linear Algebra Appl. 93 (1987), 161-170. crossref(new window)

9.
X. Shao, Z. Li, and C. Li, Modified SOR-like method for the augmented system, Int. J. Comput. Math. 84 (2007), no. 11, 1653-1662. crossref(new window)