On the perturbation of the zeros of complex polynomials

We investigate the deviation of the zeros of a polynomial. The deviation gr ows with the nth root of the perturbation of the polynomial, where n is the degree of the polynomial, and the task is to determine the factor in front of this root. We improve upon earlier results by Ostrowski and Schonhage a nd give sharp estimates. Applications are given in estimating the differenc es of root-radii, which is important for the computation of the zeros of po lynomials.