理论数学

Vol.2 No.1 (January 2012)

H-矩阵的预条件对角占优性
Preconditioned Diagonally Dominant Properties of H-Matrix

 

作者:

王学忠 , 李晓梅

 

关键词:

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

 

摘要:

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.

文章引用:

王学忠 , 李晓梅 (2012) H-矩阵的预条件对角占优性。 理论数学, 2, 39-44. doi: 10.12677/pm.2012.21008

 

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