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New inclusion sets for singular values

In this paper, for a given matrix A = ( a i j ) ∈ C n × n , in terms of r i and c i , where r i = ∑ j = 1 , j ≠ i n | a i j | , c i = ∑ j = 1 , j ≠ i n | a j i | , some new inclusion sets for singular values of the matrix are established. It is proved that the new inclusion sets are tighter than the...

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Bibliographic Details
Published in:Journal of inequalities and applications 2017-03, Vol.2017 (1), p.1-8, Article 64
Main Authors: He, Jun, Liu, Yan-Min, Tian, Jun-Kang, Ren, Ze-Rong
Format: Article
Language:English
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Summary:In this paper, for a given matrix A = ( a i j ) ∈ C n × n , in terms of r i and c i , where r i = ∑ j = 1 , j ≠ i n | a i j | , c i = ∑ j = 1 , j ≠ i n | a j i | , some new inclusion sets for singular values of the matrix are established. It is proved that the new inclusion sets are tighter than the Geršgorin-type sets (Qi in Linear Algebra Appl. 56:105-119, 1984 ) and the Brauer-type sets (Li in Comput. Math. Appl. 37:9-15, 1999 ). A numerical experiment shows the efficiency of our new results.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-017-1337-8