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H-矩阵的预条件对角占优性
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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Abstract:

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.

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