关于非Hermitian正定线性代数方程组的超松弛HSS方法

doi:10.12286/jssx.j2021-0773

计算数学 ›› 2022, Vol. 44 ›› Issue (4): 481-495.DOI: 10.12286/jssx.j2021-0773

关于非Hermitian正定线性代数方程组的超松弛HSS方法

潘春平

浙江工业职业技术学院, 绍兴 312000

收稿日期:2021-01-11 出版日期:2022-11-14 发布日期:2022-11-08
基金资助:
工业设计创新团队建设项目资助.

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潘春平. 关于非Hermitian正定线性代数方程组的超松弛HSS方法[J]. 计算数学, 2022, 44(4): 481-495.

Pan Chunping. ON THE OVER RELAXATION HSS METHOD FOR NON HERMITIAN POSITIVE DEFINITE LINEAR ALGEBRAIC EQUATIONS[J]. Mathematica Numerica Sinica, 2022, 44(4): 481-495.

ON THE OVER RELAXATION HSS METHOD FOR NON HERMITIAN POSITIVE DEFINITE LINEAR ALGEBRAIC EQUATIONS

Pan Chunping

Zhejiang Industry Polytechnic College, shaoxing, 312000, China

Received:2021-01-11 Online:2022-11-14 Published:2022-11-08

本文针对求解大型稀疏非Hermitian正定线性方程组的HSS迭代方法,利用迭代法的松弛技术进行加速,提出了一种具有三个参数的超松弛HSS方法(SAHSS)和不精确的SAHSS方法(ISAHSS),它采用CG和一些Krylov子空间方法作为其内部过程,并研究了SAHSS和ISAHSS方法的收敛性.数值例子验证了新方法的有效性.

关键词： 迭代方法, 非Hermitian正定矩阵, Hermitian和skew-Hermitian分裂, HSS方法

In this paper, efficient iterative methods for the large sparse non-Hermitian positive definite systems of linear equations, based on the Hermitian and skew-Hermitian splitting of the coefficient matrix, are studied. Based on the relaxation technique of iterative method, An over relaxed Hermitian/skew-Hermitian (SAHSS)iteration method with three parameters and its inexact version, the inexact Hermitian/skew-Hermitian (ISAHSS) iteration are proposed, which employs CG and some Krylov subspace methods as its inner process. The convergence of SAHSS and ISAHSS methods are studied. Numerical examples show the effectiveness of the new methods.

Key words: iterative methods, Non-Hermitian positive definite matrix, Hermitian and skew-Hermitian splitting, HSS method

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关于非Hermitian正定线性代数方程组的超松弛HSS方法

ON THE OVER RELAXATION HSS METHOD FOR NON HERMITIAN POSITIVE DEFINITE LINEAR ALGEBRAIC EQUATIONS

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