Gauss-Seidel iterative methods; Convergence; General H-matrices
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 H−matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with non-strictly diagonally dominant matrices and general H−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 H−matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general H−matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper.
Zhang, Cheng-yi; Ye, Dan; Zhong, Cong-Lei; and SHUANGHUA, SHUANGHUA.
"Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices",
Electronic Journal of Linear Algebra,
Volume 30, pp. 843-870.