Improved Cauchy radius for scalar and matrix polynomials

TL;DR

This paper presents an enhanced method for estimating the bounds on zeros and eigenvalues of scalar and matrix polynomials by improving the Cauchy radius through the use of suitable polynomial multipliers.

Contribution

The authors introduce a novel approach to tighten the Cauchy radius bounds for scalar and matrix polynomials using polynomial multipliers, advancing existing techniques.

Findings

Improved bounds on polynomial zeros and eigenvalues.

Enhanced accuracy of spectral radius estimates.

Applicable to a broad class of polynomials.

Abstract

We improve the Cauchy radius of both scalar and matrix polynomials, which is an upper bound on the moduli of the zeros and eigenvalues, respectively, by using appropriate polynomial multipliers.