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.

• Articles • Previous Articles Next Articles

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

Abstract

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

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.