- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Advances in Numerical Analysis
Volume 2013 (2013), Article ID 512084, 7 pages
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.
- 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.
- D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York, NY, USA, 1971.
- 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.
- R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, USA, 1962.
- 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.
- A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, NY, USA, 1979.
- A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, USA, 1994.
- O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, UK, 1994.
- 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.
- 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.
- 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).
- 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.
- 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.