理论数学  >> Vol. 5 No. 5 (September 2015)

一种H-矩阵的块预条件AOR迭代法的收敛性
Convergence on Preconditioned Block AOR Iterative Method of H-Matrix

DOI: 10.12677/PM.2015.55029, PDF, HTML, XML, 下载: 1,859  浏览: 6,022 

作者: 赵春云*:张掖中学,甘肃 张掖

关键词: H-矩阵块AOR迭代法预条件矩阵收敛性H-Matrix Block AOR Iterative Method The Preconditioned Matrix The Convergence

摘要: 本文利用块预条件技术考虑了解线性方程组Ax=b的块预条件AOR迭代法。当方程组的系数矩阵A是H-矩阵时,得出了该方法的收敛性结果。
Abstract: We consider block AOR preconditioned iterative method for solving the linear system Ax=b , using the preconditioning technology. When the coefficient matrix A is an H-matrix, the conver-gence results of the presented method are given.

文章引用: 赵春云. 一种H-矩阵的块预条件AOR迭代法的收敛性[J]. 理论数学, 2015, 5(5): 207-211. http://dx.doi.org/10.12677/PM.2015.55029

参考文献

[1] Anelli, M. and Hadjidimos, A. (2004) Block Gauss elimination followed by a classical. Iterative method for the solution of linear systems. Computational and Applied Mathematics, 163, 381-400.
http://dx.doi.org/10.1016/j.cam.2003.08.045
[2] 王学忠, 李晓梅 (2012) H-矩阵的预条件对角占优性. 理论数学, 1, 39-44.
[3] Li, W. and You, Z.Y. (1998) The multi-parameters overrelaxation method. Journal of Computational Mathematics, 16, 231-238.
[4] Varga, R.S. (1981) Matrix iterative analysis. Prentice-Hall, Englewood Cliffs.
[5] Berman, A. and Plemmons, R.J. (1994) Nonnegative matrices in the mathematical sciences. SIAM, Philadelphia.
http://dx.doi.org/10.1137/1.9781611971262
[6] Kolotilina, L.Yu. (1995) Two-sided bounds for the inverse of an H-matrix. Linear Algebra and Its Applications, 225, 117-123.
http://dx.doi.org/10.1016/0024-3795(93)00325-T
[7] 黄延祝, 杨传胜 (2007) 特殊矩阵分析及应用. 科学出版社, 北京.