Computation of dominant real roots of polynomials

Abstract

The computation of the dominant positive roots of univariate polynomials is a key step for real root isolation algorithms. We propose a new device for computing dominant real roots and compare it with other methods. For roots surpassing unity, we obtain better results than the classical estimates of Lagrange and Long-champ. We also discuss a new refined result on bounds for positive roots that can be used for all polynomials with sign changes.