广义鞍点问题基于PSS的约束预条件子

doi:10.12286/jssx.2012.2.183

计算数学 ›› 2012, Vol. 34 ›› Issue (2): 183-194.DOI: 10.12286/jssx.2012.2.183

广义鞍点问题基于PSS的约束预条件子

曹阳^1,2, 牛强³, 蒋美群¹

1. 苏州大学数学科学学院, 江苏苏州 215006;
2. 南通大学交通学院, 江苏南通 226019;
3. 西交利物浦大学数理中心, 江苏苏州 215123

收稿日期:2011-09-05 出版日期:2012-05-15 发布日期:2012-05-20
基金资助:
苏州大学国家自然科学基金预研基金(SDY2011B01),江苏省普通高校研究生创新项目(CX10B_029Z),苏州大学优秀博士学位论文选题立项(23320957),西交利物浦大学科研发展基金RDF.

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曹阳, 牛强, 蒋美群. 广义鞍点问题基于PSS的约束预条件子[J]. 计算数学, 2012, 34(2): 183-194.

Cao Yang, Niu Qiang, Jiang Meiqun. ON PSS-BASED CONSTRAINT PRECONDITIONERS FOR GENERALIZED SADDLE POINT PROBLEMS[J]. Mathematica Numerica Sinica, 2012, 34(2): 183-194.

ON PSS-BASED CONSTRAINT PRECONDITIONERS FOR GENERALIZED SADDLE POINT PROBLEMS

Cao Yang^1,2, Niu Qiang³, Jiang Meiqun¹

1. School of Mathematics Sciences, Soochow University, Suzhou 215006, Jiangsu, China;
2. School of Transportation, Nantong University, Nantong 226019, Jiangsu, China;
3. Mathematics and Physics Center, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China

Received:2011-09-05 Online:2012-05-15 Published:2012-05-20

对于(1,1)块为非Hermitian阵的广义鞍点问题,本文给出了一种基于正定和反对称分裂(Positive definite andskew-Hermitian splitting, PSS)的约束预条件子.该预条件子的(1,1)块由求解非Hermitian正定线性方程组时的PSS迭代法所构造得到.文中分析了PSS约束预条件子的一些性质并证明了预处理迭代法的收敛性.最后用数值算例验证了该预条件子的有效性.

关键词： 广义鞍点问题, 正定反对称分裂, 迭代法, 约束预条件子

In this paper, a PSS-based constraint preconditioner, in which the (1,1) block of the preconditioner is constructed by the PSS iterative method for solving the non-Hermitian positive definite linear systems, is presented for the generalized saddle point problems with non-Hermitian (1,1) blocks. The invertibility of the PSS-based constraint preconditioner is analyzed and the convergence of the preconditioned iteration method is proved. Numerical experiments are illustrated to show the efficiency of the preconditioner as well as the corresponding preconditioned iterative method.

Key words: generalized saddle point problem, PSS, iterative method, constraint preconditioner

MR(2010)主题分类:

65F10

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摘要

广义鞍点问题基于PSS的约束预条件子

ON PSS-BASED CONSTRAINT PRECONDITIONERS FOR GENERALIZED SADDLE POINT PROBLEMS

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