Semilocal convergence of two iterative methods for simultaneous computation of polynomial zeros

Abstract

In this paper we study some iterative methods for simultaneous approximation of polynomial zeros. We give new semilocal convergence theorems with error bounds for Ehrlich's and Nourein's iterations. Our theorems generalize and improve recent results of Zheng and Huang [J. Comput. Math. 18 (2000), 113--122], Petković and Herceg [J. Comput. Appl. Math. 136 (2001), 283--307] and Nedić [Novi Sad J. Math. 31 (2001), 103--111]. We also present a new sufficient condition for simple zeros of a polynomial.