Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 519017, 6 pages
http://dx.doi.org/10.1155/2014/519017
Research Article

A Preconditioned Multisplitting and Schwarz Method for Linear Complementarity Problem

School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China

Received 21 November 2013; Accepted 6 June 2014; Published 23 June 2014

Academic Editor: Changbum Chun

Copyright © 2014 Cuiyu Liu and Chen-liang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Z.-Z. Bai, “The convergence of parallel iteration algorithms for linear complementarity problems,” Computers and Mathematics with Applications, vol. 32, no. 9, pp. 1–17, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. R.-W. Cottle, J.-S. Pang, and R. E. Stone, The Linear Complementarity Problem, Academic Press, San Diego, Calif, USA, 1992. View at MathSciNet
  3. D.-H. Li, J.-P. Zeng, and Z. Zhang, “Gaussian pivoting method for solving linear complementarity problem,” Applied Mathematics—A Journal of Chinese Universities, vol. 12, no. 4, pp. 419–426, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. O. L. Mangasarian, “Solution of symmetric linear complementarity problems by iterative methods,” Journal of Optimization Theory and Applications, vol. 22, no. 4, pp. 465–485, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. Z.-Z. Bai and D. Evans, “Matrix multisplitting relaxation methods for linear complementarity problems,” International Journal of Computer Mathematics, vol. 63, no. 3-4, pp. 309–326, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. Z.-Z. Bai and D. J. Evans, “Matrix multisplitting methods with applications to linear complementarity problems: parallel asynchronous methods,” International Journal of Computer Mathematics, vol. 79, no. 2, pp. 205–232, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. Z.-Z. Bai and L.-L. Zhang, “Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems,” Numerical Algorithms, vol. 62, no. 1, pp. 59–77, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. C.-L. Li and J.-P. Zeng, “Multisplitting iteration schemes for solving a class of nonlinear complementarity problems,” Acta Mathematicae Applicatae Sinica, English Series, vol. 23, no. 1, pp. 79–90, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. Z.-Q. Luo and P. Tseng, “On the convergence of a matrix splitting algorithm for the symmetric monotone linear complementarity problem,” SIAM Journal on Control and Optimization, vol. 29, no. 5, pp. 1037–1060, 1991. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. N. Machida, M. Fukushima, and T. Ibaraki, “A multisplitting method for symmetric linear complementarity problems,” Journal of Computational and Applied Mathematics, vol. 62, no. 2, pp. 217–227, 1995. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  11. N. Zheng and J.-F. Yin, “Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem,” Numerical Algorithms, vol. 64, no. 2, pp. 245–262, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. A. Hadjidimos, D. Noutsos, and M. Tzoumas, “More on modifications and improvements of classical iterative schemes for M-matrices,” Linear Algebra and Its Applications, vol. 364, pp. 253–279, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. J. P. Milaszewicz, “Improving Jacobi and Gauss-Seidel iterations,” Linear Algebra and Its Applications, vol. 93, pp. 161–170, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. C. Liu and C. Li, “A new preconditioned generalised AOR method for the linear complementarity problem based on a generalised Hadjidimos preconditioner,” East Asian Journal on Applied Mathematics, vol. 2, pp. 94–107, 2012. View at Google Scholar · View at Zentralblatt MATH
  15. E.-L. Yip, “A necessary and sufficient condition for M-matrices and its relation to block LU factorization,” Linear Algebra and Its Applications, vol. 235, pp. 261–274, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  16. A. Berman and R.-J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1979. View at MathSciNet