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A New Preconditioned Generalised AOR Method for the Linear Complementarity Problem Based on a Generalised Hadjidimos Preconditioner

Published online by Cambridge University Press:  28 May 2015

Cuiyu Liu*
Affiliation:
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, China, 541004
Chenliang Li*
Affiliation:
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, China, 541004
*
Corresponding author. Email: liucy@guet.edu.cn
Corresponding author. Email: chenliang_li@hotmail.com
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Abstract

A new generalised Hadjidimos preconditioner and preconditioned generalised AOR method for the solution of the linear complementarity problem are presented. The convergence and convergence rate of the new method are analysed, and numerical experiments demonstrate that it is efficient.

Type
Research Article
Copyright
Copyright © Global-Science Press 2012

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References

[1]Ahn, B. H., Solution of nonsymmetric linear complementarity problems by iterative methods, J. Optim. Theory Appl., 33(1981), 185197.CrossRefGoogle Scholar
[2]Bai, Z. Z., Evans, D. J., Matrix multisplitting relaxation methods for linear complementarity problems, Int. J. Comput. Math., 63(1997), 309326.Google Scholar
[3]Bai, Z. Z., On the convergence of the multisplitting methods for the linear complementarity problem, SIAM J. Matrix Anal. Appl., 21(1999), 6778.Google Scholar
[4]Berman, A., Plemmoms, R.J., Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, 1994.Google Scholar
[5]Cottle, R. W., Sacher, R. S., On the solution of large structured linear complementarity problems: The tridiagonal case, Appl. Math. Optim., 4(1977), 321340.CrossRefGoogle Scholar
[6]Cottle, R. W., Gloub, G. H., Sacher, R. S., On the solution of large structured linear complementarity problems: The block partitioned case, Appl. Math. Optim., 4(1978), 347363.CrossRefGoogle Scholar
[7]Evans, D. J., Martins, M. M., Trigo, M. E., The AOR iterative method for new preconditioned linear systems, J. Comput. Appl. Math., 132(2001), 461466.CrossRefGoogle Scholar
[8]Frommer, A., Schwandt, H., A unified representation and theory of algebraic additive Schwarz and multisplitting methods, SIAM J. Martrix Anal. Appl. 18(1997), 893912.CrossRefGoogle Scholar
[9]Frommer, A., Szyld, D. B., H—splittings and two-stage iterative methods, Numer. Math., 63(1992), 345356.CrossRefGoogle Scholar
[10]Hadjidimos, A., Noutsos, D., Tzoumas, M., More on modifications and improvements of classical iterative schemes for M-matrices, Linear Algebra Appl., 364(2003), 253279.Google Scholar
[11]Hong, J. W., Li, Y. T., A new preanditionded AOR iterative method for L-matrices, J. Comput. Appl. Math., 229(2009), 4753.Google Scholar
[12]Li, Y., Dai, P., generalised AOR methods for linear complemenity problem, Appl. Math. Com-put., 188(2007), 718.Google Scholar
[13]Li, D. H., Zeng, J. P., Zhang, Z., Gaussian pivoting method for solving linear complementarity problem, Applied Mathematics-JCU, 12B(1997), 419426.Google Scholar
[14]Liu, Q., Chen, G., Convergence analysis of preconditioned AOR iterative method for linear systems, Mathematical Problems in Engineering, 2010(2010), 341982.Google Scholar
[15]Machida, N., Fukushima, M., Ibaraki, T., A multisplitting method for symmetric linear complementarity problems, J. Comput. Appl. Math., 62(1995), 217227.CrossRefGoogle Scholar
[16]Mangasarian, O. L., Solution of symmetric linear complementarity problems by iterative methods, J. Optim. Theory Appl., 22(1977), 465485.Google Scholar
[17]Milaszewicz, J. P., Improving Jacobi and Gauss-Seidel iterations, Linear Algebra Appl., 93(1987), 161170.Google Scholar
[18]Yip, E. L., A necessary and sufficient condition for M—matrices and its relation to block LU factorization, Linear Algebra Appl., 235(1995), 261274.Google Scholar
[19]Varga, R. S., Matrix Iterative Analysis (Second Edition), Science Press, Beijing, 2006.Google Scholar