A note on the inclusion sets for singular values

AIMS Mathematics

关键词: : ;    Singular value;    Matrix;    Inclusion sets;   

DOI  :  10.3934/Math.2017.2.315

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

In this paper, for a given matrix $A=(a_{ij}) \in \mathbb{C}^{n\times n}$, in terms of $r_i$ and $c_i$, where $ r_i= \sum\limits_{j = 1,j \ne i}^n {\left| {a_{ij} } \right|}, \ \ c_i= \sum\limits_{j = 1,j \ne i}^n {\left| {a_{ji} } \right|} $, some new inclusion sets for singular values of amatrix are established. It is proved that the new inclusion sets are tighter than the Geršgorin-type sets [1] and the Brauer-type sets [2]. A numerical experiment show the efficiency of our new results.

【 授权许可】

CC BY