On the fourth order zero-finding methods for polynomials

Abstract

Abstract. The fourth order methods for the simultaneous approximation of simple complex zeros of a polynomial are considered. The main attention is devoted to a new method that may be regarded as a modification of the well known cubically convergent Ehrlich-Aberth method. It is proved that this method has the order of convergence equals four. Two numerical examples are given to demonstrate the convergence behavior of the studied methods.