A note on a new cubically convergent one-parameter root solver

Abstract

A new one-parameter family of iterative method for solving nonlinear equations is constructed and studied. Two variants, both with cubic convergence, are developed, one for finding simple zeros and other for multiple zeros of known multiplicities. This family generates a variety of different third order methods, including Halley-like method as a special case. Four numerical examples are given to demonstrate convergence properties of the proposed methods for multiple zeros and various values of the parameter.