Bounds on polynomial roots using intercyclic companion matrices

The Frobenius companion matrix, and more recently the Fiedler companion matrices, have been used to provide lower and upper bounds on the modulus of any root of a polynomial p ( x ) . In this paper we explore new bounds obtained from taking the 1-norm and ∞-norm of a matrix in the wider class of intercyclic companion matrices. As is the case with Fiedler matrices, we observe that the new bounds from intercyclic companion matrices can improve …