H-矩阵基于外推GaussSeidel迭代法的几个等价条件

J4 ›› 2013, Vol. 48 ›› Issue (4): 65-71.

H-矩阵基于外推GaussSeidel迭代法的几个等价条件

薛秋芳1,2,高兴宝1*,刘晓光1

1. 陕西师范大学数学与信息科学学院, 陕西西安 710062;
2. 西安理工大学理学院应用数学系, 陕西西安 710054

收稿日期:2012-05-15 出版日期:2013-04-20 发布日期:2013-04-16
通讯作者: 高兴宝(1966- ),男,博士生导师,教授,主要从事智能计算方面的研究.Email:xinbaog@snnu.edu.cn
作者简介:薛秋芳(1978- ),女,博士研究生,讲师,主要从事数值计算方面的研究.Email:qiufangxue@163.com
基金资助:
国家自然科学基金资助项目（61273311,61173094）

Several equivalent conditions for H-matrix based on the extrapolated GaussSeidel iterative method

XUE Qiu-fang1,2, GAO Xing-bao1*, LIU Xiao-guang1

1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;
2. Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, Shaanxi, China

Received:2012-05-15 Online:2013-04-20 Published:2013-04-16

摘要/Abstract

摘要：

利用最优尺度矩阵及M-1N的某些估计量讨论了外推Gauss-Seidel迭代法的收敛性及其和H-矩阵的关系。基于外推Gauss-Seidel及Gauss-Seidel迭代法得到了H-矩阵的几个等价条件。同时也得到了严格对角占优矩阵,不可约对角占优矩阵及Stieltjes矩阵的GaussSeidel迭代法,外推Gauss-Seidel迭代法的相关收敛性结论。

关键词: H-矩阵;Gauss-Seidel迭代法;外推Gauss-Seidel迭代法;最优尺度矩阵;谱半径

Abstract:

The optimal scaling matrix and the estimates of some amounts of M-1N are used to discuss the convergence of the extrapolated Gauss-Seidel iteration methods and the relationship between them and H-matrices. Several equivalent conditions for the Hmatrices based on the extrapolated Gauss-Seidel and the Gauss-Seidel iterative methods are obtained. And the convergence results of the Gauss-Seidel and the extrapolated Gauss-Seidel iterative methods are given for the strictly diagonally dominant matrices, the irreducible diagonally dominant matrices and the Stieltjes matrices.

Key words: H-matrix; Gauss-Seidel iterative method; extrapolated Gauss-Seidel iterative method; optimal scaling matrix; spectral radius

薛秋芳1,2,高兴宝1*,刘晓光1. H-矩阵基于外推GaussSeidel迭代法的几个等价条件[J]. J4, 2013, 48(4): 65-71.

XUE Qiu-fang1,2, GAO Xing-bao1*, LIU Xiao-guang1. Several equivalent conditions for H-matrix based on the extrapolated GaussSeidel iterative method[J]. J4, 2013, 48(4): 65-71.

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