一种基于H-矩阵的预条件对角占优矩阵的构造方法

A Technique for Construcing Preconditioned Diagonally Dominant Matrix Based on H-Matrix

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。本文给出了一种构造预条件矩阵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。

It is well-known that most iterative methods converge for linear systems whose coefficient matrix isA a strictly diagonally dominant. WhenA is not diagonally dominant, preconditioned techniques can be employed. This paper presents a met hod to establish appropriate preconditioned matricesPandQfor transforming anH-matrix which is non-diagonally dominant matrix into a diagonally dominant matrix. Numerrical examples also show the effectiveness of this method.