Graph theoretic proofs for some results on banded inverses of M-matrices

2024/12/05 by Sanjoy Pratihar, Pratihar, S., K. C. ‎Sivakumar +1
Computer Science · Mathematics · #Matrix Theory and Algorithms #Graph theory and applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.18611

Abstract

This work concerns results on conditions guaranteeing that certain banded M-matrices have banded inverses. As a first goal, a graph theoretic characterization for an off-diagonal entry of the inverse of an M-matrix to be positive, is presented. This result, in turn, is used in providing alternative graph theoretic proofs of the following: (1) a characterization for a tridiagonal M-matrix to have a tridiagonal inverse. (2) a necessary condition for an M-matrix to have a pentadiagonal inverse. The results are illustrated by several numerical examples.

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