Approximating optimal parameters for generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) method

被引：9

作者：

Dehghan, Mehdi ^{[1
]}

Shirilord, Akbar ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran Polytech, 424 Hafez Ave, Tehran 15914, Iran

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2022年 / 41卷 / 02期

关键词：

Optimal parameter; Complex matrix; Symmetric semi-positive definite matrix; GPHSS method; Trace; Solving linear systems with complex symmetric semi-positive definite coefficient matrix; SYSTEMS;

D O I：

10.1007/s40314-021-01747-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) method is a numerical method for obtaining the solution of linear systems with complex symmetric semi-positive definite coefficient matrix. This method relates to the two relaxed parameters that should be chosen properly and is a hard task mathematically. In this study, based on the work in [J. Comput. Appl. Math. 255, 142-149 (2014)] that investigates the optimum parameter for the HSS method, we expand the results of this paper for computing optimum parameters for GPHSS method. We will show that these parameters are obtained by minimizing a function of two variables. Finally in the numerical section, we study some test problems to support the theoretical discussion.

引用

页数：23

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