文献类型：期刊文献

中文题名：非Hermitian正定线性方程组的外推的广义HSS方法

英文题名：An extrapolated and generalized HSS method for non-Hermitian positive definite linear systems

作者：吴思婷[1];鲍亮[1]

机构：[1]华东理工大学数学学院,上海200237

年份：2022

卷号：44

期号：10

起止页码：1885

中文期刊名：计算机工程与科学

外文期刊名：Computer Engineering & Science

收录：CSTPCD;;北大核心:【北大核心2020】；CSCD:【CSCD_E2021_2022】；

语种：中文

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

外文关键词：non-Hermitian positive definite linear systems;GHSS iteration method;EHSS iteration method;convergence

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。
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.