On a modification of the Ehrlich–Aberth method for simultaneous approximation of polynomial zeros

Abstract

A modified method of the fourth order for the simultaneous determination of simple complex zeros of a polynomial, which may be regarded as an extension of the Ehrlich–Aberth method, is given. This method is derived using a very simple procedure which is also applicable for the construction of a whole class of simultaneous methods. The convergence analysis of the presented method is performed under computationally verifiable initial conditions, which is of significant practical importance. Numerical results obtained by several iterative methods of the fourth order are also given.

Keywords:

• Zeros of polynomials
• Point estimation
• Fourth order methods
• Simultaneous methods
• Guaranteed convergence