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A well-known property of an M -matrix is that its inverse is elementwise nonnegative, which we write as M −1 ≥ 0. In a previous paper [Linear Algebra Appl., 434 (2011), pp. 131-143], we gave sufficient bounds on single element perturbations so that monotonicity persists for a perturbed tridiagonal M -matrix. Here we extend these results, presenting the actual maximum upper bounds on single element perturbations, as well as sufficient and necessary conditions for the maximum allowable higherdoi:10.1137/100812483 fatcat:a6vilfvypvcvfhxkcfi2eyquzy