Inverse positivity of perturbed tridiagonal M-matrices

A well-known property of an M-matrix M is that the inverse is element-wise non-negative, which we write as M-1⩾0. In this paper, we consider element-wise perturbations of non-symmetric tridiagonal M-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. Sufficient bounds are written in terms of decay estimates which characterize the decay of the elements of the inverse of the unperturbed matrix. Results for general symmetric matrices and symmetric Toeplitz matrices are obtained as special cases and compared with known results.