Predictor-corrector Halley method for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor-corrector type iterative methods for solving nonlinear equations of the type f(x) = 0 by using the technique of updating the solution. This method can be viewed as a predictor-corrector iterative Halley's method. We also consider the convergence analysis of the proposed method. To illustrate the efficiency of this new method, we give several examples and a comparison with the method of Grau and Diaz-Barrero [M. Grau, J.L. Diaz-Barrero, An improvement to Ostrowski root-finding method, Appl. Math. Comput. 173 (2006) 450-456] is given. This method can be considered as a refinement and improvement of the Halley method.