Multiple root-finding methods (Q1196848)

The paper deals with iterative algorithms for finding the roots of a real function \(f: J\to\mathbb{R}\), \(J\subset \mathbb{R}\) an interval. It is a well-known fact that convergence slows down in case of multiple zeros. The authors present a method which is proved to accelerate the convergence and simultaneously computes the multiplicity of the zero. In order to illustrate the application of this method it is applied to some wide classes including the iteration functions of Newton-Raphson, Halley and Ostrowski.