The disc separation and the eigenvalue distribution of the Schur complement of nonstrictly diagonally dominant matrices

被引：1
|
作者：
Zhang, Cheng-yi [1 ]
Wang, Weiwei [1 ]
Luo, Shuanghua [1 ]
Zhao, Jianxing [2 ]
机构：
[1] Xian Polytech Univ, Sch Sci, Xian 710048, Shaanxi, Peoples R China
[2] Guizhou Minzu Univ, Coll Sci, Guiyang 550025, Guizhou, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年
关键词：
Gersgorin disc separation; Schur complement; nonstrictly diagonally dominant matrices; eigenvalue distribution; GENERAL H-MATRICES;
D O I：
10.1186/s13660-017-1340-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The result on the Gersgorin disc separation from the origin for strictly diagonally dominant matrices and their Schur complements in (Liu and Zhang in SIAM J. Matrix Anal. Appl. 27(3): 665-674, 2005) is extended to nonstrictly diagonally dominant matrices and their Schur complements, showing that under some conditions the separation of the Schur complement of a nonstrictly diagonally dominant matrix is greater than that of the original grand matrix. As an application, the eigenvalue distribution of the Schur complement is discussed for nonstrictly diagonally dominant matrices to derive some significant conclusions. Finally, some examples are provided to show the effectiveness of theoretical results.
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页数：12
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