An improvement on two iteration methods for simultaneous determination of the zeros of a polynomial

Abstract

The Durand-Kerner and the Ehrlich† Methods of respective quadratic and cubic convergence are two of the current methods for determining simultaneously all zeros of a polynomial. By respectively including a Durand-Kerner and a Newton correction term in the above formulae, we establish two new methods-the Improved Durand-Kerner and the Improved Ehrlich.

We show that the improvement is reflected by an increase of unity in the order of convergence of each of the two methods.