The inverse positivity of perturbed tridiagonal M-matrices |
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Authors: | Jie Huang |
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Institution: | School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, PR China |
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Abstract: | 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 sufficient bounds on the perturbations so that the non-negative inverse persists. These bounds improve the bounds recently given by Kennedy and Haynes Inverse positivity of perturbed tridiagonal M-matrices, Linear Algebra Appl. 430 (2009) 2312-2323]. In particular, when perturbing the second diagonals (elements (l,l+2) and (l,l-2)) of M, these sufficient bounds are shown to be the actual maximum allowable perturbations. Numerical examples are given to demonstrate the effectiveness of our estimates. |
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Keywords: | 15A48 15A09 |
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