International Journal of Engineering and Manufacturing (IJEM)
IJEM Vol. 2, No. 4, 29 Aug. 2012
Cover page and Table of Contents: PDF (size: 284KB)
Convergence of SAOR Method for the Linear Complementarity Problems
Full Text (PDF, 284KB), PP.74-83
Views: 0 Downloads: 0
Author(s)
Xian-li Han
1,*
Dong-jin Yuan
1
Shan Jiang
1
Index Terms
Linear complementarity problem, SAOR method, Convergence, H-matrix, M-matrix
Abstract
In this paper we apply an iterative method, the SAOR method for solving the linear complementarity problem, and some sufficient conditions for the convergence of the new method are presented when the system matrix M is an M-matrix. Moreover when M is an L-matrix, we discuss the monotone convergence of it. Finally, we report the numerical results of our proposed method.
Cite This Paper
Xian-li Han,Dong-jin Yuan,Shan Jiang,"Convergence of SAOR Method for the Linear Complementarity Problems", IJEM, vol.2, no.4, pp.74-83, 2012. DOI: 10.5815/ijem.2012.04.10
Reference
[1]A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, 3rd ed., SIAM, Philadelphia, 1994.
[2]R. W. Cottle, G. H. Golub and R. S. Sacher, On the solution of large structured linear complementarity problems, Technical Report STAN-CS-74 439, Stanford University, Stanford, CA, 1974.
[3]M. D. Koulisianis and T. S. Papatheodorou, “Improving projected successive overrelaxation method for linear complementarity problems,” Appl. Numer. Math, vol. 45, no. 1, pp. 29-40, 2003.
[4]D. Yuan and Y. Song, “Modified AOR Methods for linear complementarity problem”, Appl. Math. Comput, vol. 140, no. 1, pp. 53-67, 2003.
[5]Y. Li and P. Dai, “Generalized AOR methods for linear complementarity problem,” Appl. Math. Comput, vol. 188, no.1, pp. 7-18, 2007.
[6]Z. Z. Bai and D. J. Evans, “Matrix multisplitting relaxation methods for the linear complementarity problem,” Int. J. Comput. Math, vol. 63, no. 3-4, pp. 309-326, 1997.
[7]Z. Z. Bai, “On the convergence of the multisplitting methods for the linear complementarity problem”, SIAM J. Matrix Anal. Appl, vol. 21, no. 1, pp. 67-78, 1999.
[8]M. Wu, L. Wang and Y. Song, “Preconditioned AOR iterative method for linear systems”, Appl. Numer. Math, vol. 57, no. 5-7, pp. 672-685, 2007.
[9]R. S. Varga, Matrix iterative Analysis, Springer-Verlag, New York, 2000.
[10]O. L. Mangasarian, “Solution of symmetric linear complementarity problems by iterative methods,” J. Optim. Theory Appl, vol. 22, no.4, pp. 465-485, 1977.
[11]B. H. Ahn, “Solution of nonsymmetric linear complementarity problems by iterative methods”, J. Optim. Theory Appl, vol. 33, no. 2, pp. 175-185, 1981.