Eigenvalue bounds for matrix polynomials in generalized bases

TL;DR

This paper develops new eigenvalue bounds for matrix polynomials in general bases, improving traditional bounds and demonstrating applications in engineering.

Contribution

It introduces generalized basis eigenvalue bounds for matrix polynomials, offering enhanced accuracy over classical methods.

Findings

Derived tighter eigenvalue inclusion regions.

Applicable to various engineering problems.

Showed improved bounds compared to traditional methods.

Abstract

We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.