全正矩阵的多水平预处理子  

Multilevel preconditioner of a totally positive matrix

作　　者：刘仲云 周孜 LIU Zhongyun;ZHOU Zi(School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410114

出　　处：《邵阳学院学报（自然科学版）》2019年第2期1-5,共5页Journal of Shaoyang University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11371075)

摘　　要：研究CG型方法解全正线性方程组。基于全正矩阵的Schur补也是全正矩阵这一性质,文中通过近似Schur补的方法构造多水平预处理子。数值实验表明预处理矩阵有较好的谱聚集性质,共轭梯度法求解预处理线性方程组有很好的收敛性。The object was to study preconditioned conjugate gradient method which is applied to solving totally positive linear system.Based on the fact that the Schur complement of a totally positive matrix is also totally positive,a multilevel preprocessor by approximating the Schur complement was proposed.Numerical experiments show that the spectrum of the preconditioning matrix has a good cluster,and the CG method for solving preconditioning linear system has a good convergence rate.

关 键 词：全正矩阵 SCHUR补 多水平预处理子 法方程 CG 

分 类 号：O241.6[理学—计算数学]