Bounds for the singular values of a matrix involving its sparsity pattern

The paper presents new upper and lower bounds for the singular values of rectangularmatrices 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. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 57–68.