Bounding the zeros of polynomials using the Frobenius companion matrix partitioned by the Cartesian decomposition

Abstract

In this work, Some new inequalities for the numerical radius of block $n$-by-$n$ matrices are presented. As an application, bounding of zeros of polynomials using the Frobenius companion matrix partitioned by the Cartesian decomposition approach is proved and affirmed by a numerical example showing that our approach of bounding zeros of polynomials could be very effective in comparison with the most famous and some recent results presented in the field.

15 pages