Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices
Abstract
It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with nonstrictly diagonally dominant matrices and general matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper.
Cite
@article{arxiv.1410.3196,
title = {Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices},
author = {Cheng-yi Zhang and Dan Ye and Cong-lei Zhong and Shuanghua Luo},
journal= {arXiv preprint arXiv:1410.3196},
year = {2014}
}