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 ALAMT  Vol.5 No.2 , June 2015
Inverse Nonnegativity of Tridiagonal M-Matrices under Diagonal Element-Wise Perturbation
Mohamed A. Ramadan1*, Mahmoud M. Abu Murad2
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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
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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