About this Journal Submit a Manuscript Table of Contents
Advances in Numerical Analysis
Volume 2013 (2013), Article ID 512084, 7 pages
http://dx.doi.org/10.1155/2013/512084
Research Article

Some Results on Preconditioned Mixed-Type Splitting Iterative Method

1Department of Mathematics, Qingdao University of Science and Technology, Qingdao 266061, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China

Received 20 June 2013; Revised 14 September 2013; Accepted 27 September 2013

Academic Editor: Zhong-Zhi Bai

Copyright © 2013 Guangbin Wang and Fuping Tan. 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. G. H. Cheng, T. Z. Huang, and S. Q. Shen, “Note to the mixed-type splitting iterative method for Z-matrices linear systems,” Journal of Computational and Applied Mathematics, vol. 220, no. 1-2, pp. 1–7, 2008. View at Publisher · View at Google Scholar · View at Scopus
  2. D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York, NY, USA, 1971.
  3. H. Schneider, “Theorems on M-splittings of a singular M-matrix which depend on graph structure,” Linear Algebra and Its Applications C, vol. 58, pp. 407–424, 1984. View at Scopus
  4. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, USA, 1962.
  5. W. Li and W. Sun, “Modified Gauss-Seidel type methods and Jacobi type methods for Z-matrices,” Linear Algebra and Its Applications, vol. 317, no. 1–3, pp. 227–240, 2000. View at Scopus
  6. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1979.
  7. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, USA, 1994.
  8. O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, UK, 1994.
  9. T. Z. Huang, G. H. Cheng, and X. Y. Cheng, “Modified SOR-type iterative method for Z-matrices,” Applied Mathematics and Computation, vol. 175, no. 1, pp. 258–268, 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. Z.-Z. Bai, “On the comparisons of the multisplitting unsymmetric aor methods for M-matrices,” Calcolo, vol. 32, no. 3-4, pp. 207–220, 1995. View at Publisher · View at Google Scholar · View at Scopus
  11. Z.-Z. Bai, “The generalized Stein-Rosenberg type theorem for the PDAOR-method,” Bulletin of the Institute of Mathematics Academia Sinica, vol. 19, pp. 329–335, 1997 (Chinese).
  12. Z.-Z. Bai, “A class of parallel decomposition-type relaxation methods for large sparse systems of linear equations,” Linear Algebra and Its Applications, vol. 282, no. 1–3, pp. 1–24, 1998. View at Scopus
  13. Z.-Z. Bai and R. Nabben, “Some properties of the block matrices in the parallel decomposition-type relaxation methods,” Applied Numerical Mathematics, vol. 29, no. 2, pp. 167–170, 1999. View at Scopus