On monotonicity-preserving perturbations of $M$-matrices

TL;DR

This paper derives an explicit analytical condition on perturbations to an M-matrix that guarantees the resulting matrix remains monotonic, aiding stability analysis in numerical methods.

Contribution

It provides a new explicit sufficient condition on perturbations of M-matrices to preserve their monotonicity property.

Findings

Derived an explicit condition for perturbations maintaining M-matrix monotonicity

The condition helps in stability analysis of numerical algorithms involving M-matrices

Enhances understanding of perturbation effects on M-matrix properties

Abstract

We obtain an explicit analytical sufficient condition on $E$ that ensures the monotonicity of the matrix $M+E$, where $M$ is an $M$-matrix.