Exclusion sets for eigenvalues of matrices

TL;DR

This paper introduces two new Brauer-type eigenvalue inclusion sets that are tighter than the classical Brauer set, helping to more precisely locate all eigenvalues of a matrix.

Contribution

The paper develops two novel Brauer-type eigenvalue exclusion sets that improve eigenvalue localization by excluding regions without eigenvalues, and proves their containment within the classical Brauer set.

Findings

New eigenvalue inclusion sets are tighter than the classical Brauer set.

The new sets are proven to be contained within the Brauer set.

The methods improve eigenvalue localization accuracy.

Abstract

To locate all eigenvalues of a matrix more precisely, we exclude some sets which do not include any eigenvalue of the matrix from the well-known Brauer set to give two new Brauer-type eigenvalue inclusion sets. And it is also shown that the new sets are contained in the Brauer set.