Inverse Nonnegativity of Tridiagonal M-Matrices under Diagonal Element-Wise Perturbation

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Ramadan, M. and Abu Murad, M. (2015) Inverse Nonnegativity of Tridiagonal M-Matrices under Diagonal Element-Wise Perturbation. Advances in Linear Algebra & Matrix Theory, 5, 37-45. doi: 10.4236/alamt.2015.52004.

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