一类非对称结构线性方程组的子结构预处理子(英文)  

Substructured preconditioners for a class of nonsymmetric structured systems of linear equations

作　　者：曹阳[1,2] 牛强[3] 蒋美群[1] 

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 [3]西交利物浦大学数理中心,江苏苏州215123

出　　处：《应用数学与计算数学学报》2012年第4期437-448,共12页Communication on Applied Mathematics and Computation

基　　金：supported by the National Natural Science Pre-Research Foundation(SDY2011B01);the College Postgraduate Research and Innovation Project of Jiangsu Province(CX10B-029Z);the Nominated Excellent Thesis for PHD Candidates Program of Soochow University(23320957)

摘　　要：针对一类具结构的非对称线性方程组提出了一类子结构预处理子,该预处理子只保留了约束条件的一半项.研究表明,预处理矩阵只有三个离散的特征值.为了避免计算Schur补的逆,还给出了正则化的子结构预处理子,同样对预处理矩阵进行了谱分析.这些结果将Zhou和Niu(Zhou J T,Niu Q.Substructure preconditioners for a class of structuredlinear systems of equations.Math.Comput.Model.,2010,52:1547-1553)的结果推广到非对称结构线性方程组.数值算例验证了提出的子结构预处理子的有效性.A substructured preconditioner is proposed for a class of nonsymmetric structured linear systems of equations. This preconditioner keeps only half of the constraint terms. Spectral analysis shows that the preconditioned matrix has only three distinct eigenvalues. To avoid computing the Schur complement, a regularized variant is considered. The spectrum is also analyzed. These theoretical results extend the previous ones （Zhou J T, Niu Q. Substructure preconditioners for a class of structured linear systems of equations. Math. Comput. Model., 2010, 52： 1547-1553）. Some numerical examples are presented to show the effectiveness of the proposed preconditioners.

关 键 词：线性方程组 预处理子 广义极小残量法 谱分析 最小多项式 

分 类 号：O241.6[理学—计算数学]