Some Simple Estimates for the Singular Values of Matrices

Abstract

We first provide a simple estimate for ∥A −1‖∞ and ‖A −1‖1 of a strictly diagonally dominant matrix A. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scaling with a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness of the new bounds.