Some bounds for extreme singular values of a complex matrix

In this study we mainly obtained upper and lower bounds for extreme singular values of an n × n complex matrix. Moreover, as an application of this, we got bounds for extreme singular values of Hilbert and Cauchy–Hankel matrices as in the forms H = ( 1 / ( i + j - 1 ) ) i , j = 1 n and H n = [ 1 / (...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-10, Vol.218 (3), p.762-765
Main Authors: Maden, ADilek, Cevik, ASinan
Format: Article
Language:English
Subjects:
Cauchy–Hankel matrix
Computation
Extreme values
Hilbert matrix
Lower bound
Lower bounds
Mathematical analysis
Mathematical models
Matrices
Singular value
Theorems
Upper bound
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Summary:In this study we mainly obtained upper and lower bounds for extreme singular values of an n × n complex matrix. Moreover, as an application of this, we got bounds for extreme singular values of Hilbert and Cauchy–Hankel matrices as in the forms H = ( 1 / ( i + j - 1 ) ) i , j = 1 n and H n = [ 1 / ( g + ( i + j ) h ) ] i , j = 1 n , respectively. We note that the bounds obtained in this paper are more effective than the bounds presented in the paper [2, Theorem 2].
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.03.073