Persistently positive inverses of perturbed M-matrices

A well known property of an M-matrix A is that the inverse is element-wise non-negative, which we write as A−1 ⩾ 0. In this paper we consider perturbations of M-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The bounds are written in terms of decay estimates which characterize the decay (along rows) of the elements of the inverse matrix. We obtain results for diagonal and rank-1 perturbations of symmetric tridiagonal M-matrices and rank-1 perturbations of non-symmetric tridiagonal M-matrices.