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Keywords Abstract

Preconditioned Diagonally Dominant Properties of H-Matrix

DOI: 10.12677/pm.2012.21008, PP. 39-44

Keywords: 迭代法;H-矩阵;预条件矩阵;对角占优性
Iterative Method
, H-Matrix, Preconditioned Matrix, Diagonally Dominant Properties

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对于线性方程组Ax=b ,当A是严格对角占优矩阵时大部分迭代法都收敛。当A不是对角占优矩阵时,预条件技术常被采用。本文给出了一种选取预条件矩阵P和Q的方法,把一个非对角占优的H-矩阵转化为严格对角占优矩阵。数值例子也说明了该方法的有效性。
It is well-known that most iterative methods converge for linear system whose coefficient matrix A is strictly diagonally dominant. When A is not diagonally dominant, preconditioned techniques can be em- ployed. This paper presents a method to establish appropriate preconditioned matrices P and Q for transfor- ming an H-matrix which is non-diagonally dominant matrix into the diagonally dominant matrix. Numerical examples also show the effectiveness of this method.


[1]  刑志栋, 曹建荣. 矩阵数值分析[M]. 西安: 陕西科学技术出版社, 2005.
[2]  张凯院, 徐仲. 数值代数[M]. 北京: 科学出版社, 2006.
[3]  陈公宁. 矩阵理论与应用[M]. 北京: 科学出版社, 2007.
[4]  黄廷祝, 杨传胜. 特殊矩阵分析及应用[M]. 北京: 科学出版社, 2007.
[5]  王学忠, 黄廷祝, 李良等. H-矩阵方程组的预条件迭代法[J]. 计算数学, 2007, 29(1): 89-96.


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