| Shi-Liang Wu |
Ting-Zhu Huang† |
School of Applied Mathematics
University of Electronic Science and Technology of China
Chengdu
Sichuan 610054
P.R. China
wushiliang1999@126.com |
School of Applied Mathematics
University of Electronic Science and Technology of China
Chengdu
Sichuan 610054
P.R. China
tzhuang@uestc.edu.cn
tingzhuhuang@126.com |
|
|
Received 14 April, 2007; revised 22 October, 2007
|
Abstract
Both Evans et al. and Li et al. have presented preconditioned methods for linear systems to improve the convergence rates of AOR-type iterative schemes. In this paper, we present a new preconditioner. Some comparison theorems on preconditioned iterative methods for solving L-matrix linear systems are presented. Comparison results and a numerical example show that convergence of the preconditioned Gauss–Seidel method is faster than that of the preconditioned AOR iterative method.
Download the article in PDF format (size 120 Kb)
| 2000 Mathematics Subject Classification:
primary 65F10; secondary 15A06
|
| (Metadata: XML, RSS, BibTeX) |
MathSciNet:
MR2376??? |
| †indicates author for correspondence |
References
-
A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences (SIAM, Philadelphia, PA, 1994).
MR1298430
-
D. J. Evans, M. M. Martins and M. E. Trigo, “The AOR iterative method for new preconditioned linear systems”, J. Comput. Appl. Math. 132 (2001) 461–466.
MR1840641
-
A. D. Gunawardena, S. K. Jain and L. Snyder, “Modified iteration methods for consistent linear systems”, Linear Algerbra Appl. 154–156 (1991) 123–143.
MR1113142
-
A. Hadjimos, “Accelerated overelaxation method”, Math. Comp. 32 (1978) 149–157.
MR483340
-
T. Z. Huang, G. H. Cheng and X. Y. Cheng, “Modified SOR-type iterative method for Z-matrices”, Appl. Math. Comput. 175 (2006) 258–268.
MR2216339
-
Y. T. Li, C. X. Li and S. L. Wu, “Improving AOR method for consistent linear systems”, Appl. Math. Comput. 186 (2007) 379–388.
MR2316522
-
J. P. Milaszewicz, “Improving Jacobi and Gauss–Seidel iterations”, Linear Algebra Appl. 93 (1987) 161–170.
MR898552
-
R. S. Varga, Matrix iterative analysis (Prentice-Hall, Englewood Cliffs, New York, 1962).
MR158502
-
Z. D. Wang and T. Z. Huang, “The upper Jacobi and upper Gauss–Seidel type iterative methods for preconditoned linear systems”, Appl. Math. Lett. 19 (2006) 1029–1036.
MR2246171
-
D. M. Young, Iterative solution of large linear systems (Academic Press, New York–London, 1971).
MR305568
|
|
