A New Lower Bound for the Smallest Singular Value

Abstract

© University of Nis. All rights reserved. The aim of this paper is to obtain new lower bounds for the smallest singular value for some special subclasses of nonsingular H-matrices. This is done in two steps: first, unifying principle for deriving new upper bounds for the norm 1 of the inverse of an arbitrary nonsingular H-matrix is presented, and then, it is combined with some well-known upper bounds for the infinity norm of the inverse. The importance and efficiency of the results are illustrated by an example from ecological modelling, as well as on a type of large-scale matrices posessing a block structure, arising in boundary value problems.