Bounds for the singular values of a matrix involving its sparsity pattern. (Russian, English) Zbl 1081.15529

Kolotilina, L. Yu.

Zap. Nauchn. Semin. POMI 323, 57-68 (2005); translation in J. Math. Sci., New York 137, No. 3, 4794-4800 (2007).

Summary: 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.

MSC:

15A42	Inequalities involving eigenvalues and eigenvectors
15B48	Positive matrices and their generalizations; cones of matrices

Keywords:

upper and lower bounds; singular values; rectangular matrix; matrix sparsity pattern; Perron root; nonnegative matrix; Ostrowski-Brauer theorem; eigenvalue inclusion regions