AIMS Mathematics, 2017, 2(2): 315-321. doi: 10.3934/Math.2017.2.315

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A note on the inclusion sets for singular values

School of mathematics, Zunyi Normal College, Zunyi, Guizhou, 563006, P.R. China

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 a matrix 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.
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Copyright Info: © 2017, Jun He, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

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