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On the fourth order zero-finding methods for polynomials

Ilić Snežana M. (Faculty of Science and Mathematics, University of Niš)
Rančić Lidija (Faculty of Electronic Engineering, University of Niš)

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.

Keywords: zeros of polynomials, fourth order methods, simultaneous methods, convergence