Two-step iterative methods for nonlinear equations

摘要

In recent years several iterative methods have been suggested and analyzed for solving nonlinear equation f(x) = 0. All these methods can be classified as one-step and two-step methods. In this paper, we consider and analyze two-step iterative methods for solving nonlinear equations. It is shown that two-step iterative methods are more efficient than one-step methods including Newton method. Several numerical examples are given to illustrate this comparison. Our results can be viewed as important refinement and improvement of the previously known results.