A note on a classical bound for the moduli of all zeros of a polynomial

Abstract

Considers the monic polynomial f(z):=z/sup n/+a/sub n-1/z/sup n-1/+. . .+a/sub 0/ in the complex variable z with complex coefficients. Under the assumption that the nonleading coefficients of f lie in the disk mod z mod <or=A the authors give an estimate for the smallest disk mod z mod <or=R containing all zeros of f. The estimate has a guaranteed precision of a few percent. They proceed similarly to obtain a zero-free disk mod z mod <or=r.<<ETX>>