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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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Published in: | Journal of inequalities and applications 2017-03, Vol.2017 (1), p.1-8, Article 64 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 1029-242X 1025-5834 1029-242X |
DOI: | 10.1186/s13660-017-1337-8 |