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

Mohamed A. Ramadan^1*, Mahmoud M. Abu Murad²

¹Department of Mathematics, Faculty of Science, Menoufia University, Shebeen El-Kom, Egypt.
²Department of Mathematics, Faculty of Science, Zagazig University, Ash Sharqiyah, Egypt.

DOI: 10.4236/alamt.2015.52004                

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.

Keywords

Totally Positive Matrix, Totally Nonnegative Matrix, Tridiagonal Matrices, Compound Matrix, Element-Wise Perturbations

Conflicts of Interest

The authors declare no conflicts of interest.

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