Theorems on Schur complement of block diagonally dominant matrices and their application in reducing the order for the solution of large scale linear systems

被引:21
作者
Liu, Jianzhou [1 ]
Huang, Zhuohong [1 ]
Zhu, Li [1 ]
Huang, Zejun [1 ]
机构
[1] Xiangtan Univ, Dept Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
基金
中国国家自然科学基金;
关键词
I-(II-)Block comparison matrix; I-(II-)Block strictly diagonally dominant matrix; I-(II-)Block strictly doubly diagonally dominant matrix; Schur complement; Gersgorin's theorem; H-MATRICES;
D O I
10.1016/j.laa.2011.05.023
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We firstly consider the block dominant degree for I-(II-)block strictly diagonally dominant matrix and their Schur complements, showing that the block dominant degree for the Schur complement of an I-(II-)block strictly diagonally dominant matrix is greater than that of the original grand block matrix. Then, as application, we present some disc theorems and some bounds for the eigenvalues of the Schur complement by the elements of the original matrix. Further, by means of matrix partition and the Schur complement of block matrix, based on the derived disc theorems, we give a kind of iteration called the Schur-based iteration, which can solve large scale linear systems though reducing the order by the Schur complement and the numerical example illustrates that the iteration can compute out the results faster. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:3085 / 3100
页数:16
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