# Lower bounds of the minimum eigenvalue for $M$-matrices

## TL;DR

This paper introduces new convergent sequences of lower bounds for the minimum eigenvalue of M-matrices, demonstrating improved accuracy over existing bounds through theoretical proofs and numerical examples.

## Contribution

It provides novel sequences of lower bounds that are proven to converge and are more accurate than previous bounds for M-matrices.

## Key findings

- Sequences are proven to be convergent.
- Numerical examples show improved accuracy.
- Bounds can reach the true eigenvalue in some cases.

## Abstract

Some monotone increasing sequences of the lower bounds for the minimum eigenvalue of $M$-matrices are given. It is proved that these sequences are convergent and improve some existing results. Numerical examples show that these sequences are more accurate than some existing results and could reach the true value of the minimum eigenvalue in some cases.