非Hermitian正定线性方程组的外推的广义HSS方法

计算机工程与科学 ›› 2022, Vol. 44 ›› Issue (10): 1885-1892.

非Hermitian正定线性方程组的外推的广义HSS方法

吴思婷，鲍亮

(华东理工大学数学学院,上海 200237)

收稿日期:2021-03-21 修回日期:2021-05-20 接受日期:2022-10-25 出版日期:2022-10-25 发布日期:2022-10-28

An extrapolated and generalized HSS method for non-Hermitian positive definite linear systems

WU Si-ting,BAO Liang

（School of Mathematics,East China University of Science and Technology,Shanghai 200237,China）

Received:2021-03-21 Revised:2021-05-20 Accepted:2022-10-25 Online:2022-10-25 Published:2022-10-28

摘要/Abstract

摘要： 探讨了如何高效求解非Hermitian正定线性方程组，提出了一种外推的广义Hermitian和反Hermitian (EGHSS) 迭代方法。首先，根据矩阵的广义Hermitian和反Hermitian分裂，构造出了一种新的非对称的二步迭代格式。接着，理论分析了新方法的收敛性，并给出了新方法收敛的充要条件。数值实验结果表明，在处理某些问题时，EGHSS迭代方法比GHSS迭代方法和EHSS迭代方法更有效。

关键词: 非Hermitian正定线性方程组, GHSS迭代方法, EHSS迭代方法, 收敛性

Abstract: How to efficiently solve non-Hermitian positive definite linear systems is discussed, and an extrapolated and generalized Hermitian and skew-Hermitian splitting iteration method (EGHSS) is proposed. Firstly, the method constructs a new asymmetric two-step iterative scheme based on the generalized Hermitian and skew-Hermitian splitting iteration. Secondly, the convergence of the new method is theoretically analyzed, and the necessary and sufficient conditions for the convergence are given. Finally, numerical experiments show that the EGHSS iteration method is more effective than the GHSS iteration method and the EHSS iteration method in dealing with some problems.

Key words: non-Hermitian positive definite linear systems；GHSS iteration method；EHSS iteration method；convergence ,

吴思婷, 鲍亮. 非Hermitian正定线性方程组的外推的广义HSS方法[J]. 计算机工程与科学, 2022, 44(10): 1885-1892.

WU Si-ting, BAO Liang. An extrapolated and generalized HSS method for non-Hermitian positive definite linear systems[J]. Computer Engineering & Science, 2022, 44(10): 1885-1892.