Modified Householder iterative method for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method for solving nonlinear equations of the type f(x)=0f(x)=0. This new method includes the two-step Newton method as a special case. We show that this new two-step method is a sixth-order convergent method. Several examples are given to illustrate the efficiency of this new method and its comparison with other sixth-order methods. This method can be considered as a significant improvement of the Newton method and its variant forms.