IMPROVED RELAXED POSITIVE-DEFINITE AND SKEW-HERMITIAN SPLITTING PRECONDITIONERS FOR SADDLE POINT PROBLEMS

被引：12

作者：

Cao, Yang ^{[1
]}

Ren, Zhiru ^{[2
]}

Yao, Linquan ^{[3
]}

机构：

[1] Nantong Univ, Sch Transportat, Nantong 226019, Peoples R China

[2] Cent Univ Finance & Econ, Sch Stat & Math, Beijing 100081, Peoples R China

[3] Soochow Univ, Sch Urban Rail Transportat, Suzhou 215006, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL MATHEMATICS | 2019年 / 37卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Saddle point problems; Preconditioning; RPSS preconditioner; Eigenvalues; Krylov subspace method; DIMENSIONAL FACTORIZATION PRECONDITIONER; OPTIMAL PARAMETERS; ITERATION METHODS;

D O I：

10.4208/jcm.1710-m2017-0065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a class of improved relaxed positive-definite and skew-Hermitian splitting (IRPSS) preconditioners for saddle point problems. These preconditioners are easier to be implemented than the relaxed positive-definite and skew-Hermitian splitting (RPSS) preconditioner at each step for solving the saddle point problem. We study spectral properties and the minimal polynomial of the IRPSS preconditioned saddle point matrix. A theoretical optimal IRPSS preconditioner is also obtained. Numerical results show that our proposed IRPSS preconditioners are superior to the existing ones in accelerating the convergence rate of the GMRES method for solving saddle point problems.

引用

页码：95 / 111

页数：17

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