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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Keywords Singular value; Matrix; Inclusion sets

Citation: Jun He, Yan-Min Liu, Jun-Kang Tian, Ze-Rong Ren. A note on the inclusion sets for singular values. AIMS Mathematics, 2017, 2(2): 315-321. doi: 10.3934/Math.2017.2.315


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This article has been cited by

  • 1. L. Yu. Kolotilina, A New Subclass of the Class of Nonsingular H $$ \mathcal{H} $$ -Matrices and Related Inclusion Sets for Eigenvalues and Singular Values, Journal of Mathematical Sciences, 2019, 10.1007/s10958-019-04398-4

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