Inequalities for the minimum eigenvalue of M-matrices

Abstract

Let A be a nonsingular M-matrix, and τ(A) denote its minimum eigenvalue. Shivakumar et al. [SIAM J. Matrix Anal. Appl., 17(2):298-312, 1996] presented some bounds of τ(A) when A is a weakly chained diagonally dominant M-matrix. The present paper establishes some new bounds of τ(A) for a general nonsingular M-matrix A. Numerical examples show that the results obtained are an improvement over some known results in certain cases.