The inverse positivity of perturbed tridiagonal M-matrices

✍ Scribed by Jie Huang; Ting-Zhu Huang

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 181 KB
• Volume: 434
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.08.012

✦ Synopsis

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 (2009Appl. 430 ( ) 2312Appl. 430 ( -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.