A note on some recent methods for solving nonlinear equations

摘要

In this note we present some comments on the recent results concerning iterative methods for solving nonlinear equations. In the first part we compare a new method [N. Ujević, A method for solving nonlinear equations, Appl. Math. Comput. 174 (2006) 1416–1426] with the Newton and Ostrowski method, including an extensive analysis of numerical results together with the choice of initial approximations, and the computational efficiency of the considered methods. In the second part we give a list of recently derived root-finding methods and we study the question of priority; namely, we find out that all reviewed methods were already derived at the beginning of the 60s of the last century, one of them dates from the 18th century. Some remarks on the comparison analysis and the application of iteration methods are included.