On the modification of the preconditioned AOR iterative method for linear system

Document Type: Research Articles

Authors

1 دانشگاه آزاد اصفهان. خوراسگان

2 دانشگاه آزاد خوراسگان

Abstract

In this paper, we will present a modification of the preconditioned AOR-type method for solving the linear system. A theorem is given to show the convergence rate of modification of the preconditioned AOR methods that can be enlarged than the convergence AOR method.

[1] A. Berman, R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic
Press, New York, 1979.
[2] A. D. Gunawardena, S. K. Jain, L. Snyder, Modified iterative methods for consistent linear
systems, Lin. Alg. Appl. 154-156 (1991) 123-143.
[3] A. Hadjidimos, Accelerated overrelaxation method, Appl. Math. Comput. 32 (1978) 149–
157.
[4] T. Kohno, H. Kotakemori, Improving the modified Gauss-Seidel method for Z-matrices,
Lin. Alg. Appl. 267 (1997) 113-123.
[5] H. Kotakemori, H. Niki, N. Okamoto, Accelerated iterative method for Z-matrices, J.
Comput. App. Math. 75 (1996) 87-97.
[6] J. Li, T. Z. Huang, Preconditioned Methods of Z-matrices, Acta. Math. Sci. 25 (2005) 5-10.
[7] W. Li, W. W. Sun, Modified Gauss-Seidel type methods and Jacobi type methods for Z-
matrices, Lin. Alg. Appl. 317 (200) 227-240.
[8] Y. Z. Song, Comparisons of nonnegative splittings of matrices, Lin. Alg. Appl. 154-156
(1991) 433-455.
[9] Y. Z. Song, Comparison theorems for splittings of matrices, Num. Math. 92 (2002) 563-
591.
[10] R. S.Varga, Matrix iterative analysis, prentice-hall, Englewood Cliffs, NJ, 1962; Springer
series in computational mathematics, 27, Speringer-Verlag, Berlin,2000.
[11] G. Wang, N. Zhang, F. Tan, A new preconditioned AOR method for Z-matrices, Wor.
Aca. Sci. Engin. Tech. 67 ( 2010) 572-574.

[12] M. Wu, L.Wang, Y.Song, Preconditioned AOR iterative method for linear systems, Appl.
Num. Math. 57 (2007) 672-685.
[13] D. M. Young, Iterative solution of large linear systems, Academic Press,
New York, 1971.
[14] Y. Zhang, T. Z. Huang, X. Liu, Gauss type preconditioning techniques for linear system,
Appl. Math. Comput. 188 (2007) 612-633.