Geodesic
Bounds for the singular values of a matrix involving its sparsity pattern
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 57-68 
L. Yu. Kolotilina. Bounds for the singular values of a matrix involving its sparsity pattern. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 57-68. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a6/
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     author = {L. Yu. Kolotilina},
     title = {Bounds for the singular values of a~matrix involving its sparsity pattern},
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     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper presents new upper and lower bounds for the singular values of a rectangular matrix explicitly involving the matrix sparsity pattern. These bounds are based on an upper bound for the Perron root of a nonnegative matrix and on the sparsity-dependent version of the Ostrowski–Brauer theorem on eigenvalue inclusion regions.

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