广义鞍点问题的松弛维数分解预条件子  

A RELAXED DIMENSIONAL FACTORIZATION PRECONDITIONER FOR GENERALIZED SADDLE POINT PROBLEMS

作　　者：曹阳[1,2] 谈为伟[2] 蒋美群[2] 

机构地区：[1]南通大学交通学院,江苏南通226019 [2]苏州大学数学科学学院,江苏苏州215006

出　　处：《计算数学》2012年第4期351-360,共10页Mathematica Numerica Sinica

基　　金：苏州大学国家自然科学基金预研基金(SDY2011B01)

摘　　要：本文将Benzi等提出的松弛维数分解(Relaxed dimensional factorization,RDF)预条件子进一步推广到广义鞍点问题上,并称为GRDF(Generalized RDF)预条件子.该预条件子可看做是用维数分裂迭代法求解广义鞍点问题而导出的改进维数分裂(Modified dimensional split,MDS)预条件子的松弛形式,它相比MDS预条件子更接近于系数矩阵,因而结合Krylov子空间方法(如GMRES)有更快的收敛速度.文中分析了GRDF预处理矩阵特征值的一些性质,并用数值算例验证了新预条件子的有效性.In this paper, the RDF （Relaxed dimensional factorization） preconditioner, which was proposed by Benzi et al., is extended to solve generalized saddle point problems. The new preconditioner is called GRDF （Generalized RDF） preconditioner and can be viewed as a relaxed form of the MDS （Modified dimensional split） preconditioner, which is induced by the dimensional splitting iteration methods for solving generalized saddle point problems. The GRDF preconditioner is much closer to the coefficient matrix than the MDS preconditioner. Thus the GRDF preconditioner may be better than the MDS preconditioner when they are used in some Krylov subspace methods （such as GMRES）. Spectrum properties of the GRDF preconditioned matrix are studied. Numerical experiments are illustrated to show the efficiency of the new preconditioner.

关 键 词：广义鞍点问题 维数分裂迭代法 预处理 特征值 

分 类 号：O241.6[理学—计算数学]