On the perturbation of the zeros of complex polynomials

We investigate the deviation of the zeros of a polynomial. Thedeviation grows with the nth root of the perturbation of thepolynomial, where n is the degree of the polynomial, and thetask is to determine the factor in front of this root. We improveupon earlier results by Ostrowski and Schönhage and givesharp estimates. Applications are given in estimating the differencesof root-radii, which is important for the computation of thezeros of polynomials.