TITLE:
Inverse Nonnegativity of Tridiagonal M-Matrices under Diagonal Element-Wise Perturbation
AUTHORS:
Mohamed A. Ramadan, Mahmoud M. Abu Murad
KEYWORDS:
Totally Positive Matrix, Totally Nonnegative Matrix, Tridiagonal Matrices, Compound Matrix, Element-Wise Perturbations
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.5 No.2,
June
9,
2015
ABSTRACT: One of the most important properties of M-matrices is element-wise non-negative of its inverse. In this paper, we consider element-wise perturbations of tridiagonal M-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The largest interval is given by which the diagonal entries of the inverse of tridiagonal M-matrices can be perturbed without losing the property of total nonnegativity. A numerical example is given to illustrate our findings.