关于非Hermitian正定线性代数方程组的超松弛HSS方法  

ONTHEOVERRELAXATIONHSS METHODFOR NONHERMITIANPOSITIVEDEFINITE LINEARALGEBRAICEQUATIONS

作　　者：潘春平[1] Pan Chunping(Zhejiang Industry Polytechnic College,shaocing,312000,China)

机构地区：[1]浙江工业职业技术学院,绍兴312000

出　　处：《计算数学》2022年第4期481-495,共15页Mathematica Numerica Sinica

基　　金：工业设计创新团队建设项目资助.

摘　　要：本文针对求解大型稀疏非Hermitian正定线性方程组的IISS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(TSAHSS),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.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,A n 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.

关 键 词：迭代方法 非Hermitian正定矩阵 Hermitian和skew-Hermitian分裂 HSS方法 

分 类 号：O241.6[理学—计算数学]