Geodesic
Inclusion sets for the singular values of a~rectangular matrix
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 94-105

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The paper generalizes certain inclusion sets for the singular values of a square matrix to the case of an $m\times n$ matrix. In particular, it is shown that under a nonrestrictive assumption on the ordering of the matrix columns (if $m$) or the matrix rows (if $m>n$), a natural counterpart of the Gerschgorin theorem on the eigenvalue location is valid. Bibl. – 14 titles. 
@article{ZNSL_2008_359_a8,
     author = {L. Yu. Kolotilina},
     title = {Inclusion sets for the singular values of a~rectangular matrix},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {94--105},
     publisher = {mathdoc},
     volume = {359},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a8/}
}
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L. Yu. Kolotilina. Inclusion sets for the singular values of a~rectangular matrix. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 94-105. http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a8/