ANZIAM J. 49 (2007), no. 2, pp. 281–292.
A modified AOR-type iterative method for L-matrix linear systems
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.

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2000 Mathematics Subject Classification: primary 65F10; secondary 15A06
(Metadata: XML, RSS, BibTeX) MathSciNet: MR2376???
†indicates author for correspondence

References

  1. A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sciences (SIAM, Philadelphia, PA, 1994). MR1298430
  2. 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
  3. 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
  4. A. Hadjimos, “Accelerated overelaxation method”, Math. Comp. 32 (1978) 149–157. MR483340
  5. 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
  6. 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
  7. J. P. Milaszewicz, “Improving Jacobi and Gauss–Seidel iterations”, Linear Algebra Appl. 93 (1987) 161–170. MR898552
  8. R. S. Varga, Matrix iterative analysis (Prentice-Hall, Englewood Cliffs, New York, 1962). MR158502
  9. 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
  10. D. M. Young, Iterative solution of large linear systems (Academic Press, New York–London, 1971). MR305568