New efficient and accurate bounds for zeros of a polynomial based on similarity of companion complex matrices

Abstract

In this paper, we present new bounds for the zeros of polynomials with numerical and matrix coefficients and show that these bounds are effective and more accurate for polynomials that have small differences between their coefficients. To get our main results, we apply the similarity of matrices and matrix inequalities including the numerical radius and matrix norms. Finally, some illustrated examples are given and discussed.