Convergence on gauss-seidel iterative methods for linear systems with general H−matrices

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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 H−matrices (generalized strictly diagonally dominant ma- trices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with nonstrictly 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.

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Zhang, C. Y., Ye, D., Zhong, C. L., & Luo, S. (2015). Convergence on gauss-seidel iterative methods for linear systems with general H−matrices. Electronic Journal of Linear Algebra, 30(1), 843–870. https://doi.org/10.13001/1081-3810.1972

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