FAMILI METODE ITERASI BERORDE TIGA UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR

Abstract

We discuss a family of iterative methods derived by giving a weight function recur-sively to the corrector of Newton’s method, which is a review of article of Herceg and Herceg publised on [Applied Mathematics and Computation, 87 (2010), 2533–2541]. Weighting with a specific index produces Super-Halley’s method. Analytically it is shown that the order of the convergence of the method is three. Furthermore, this iteration method requires four function evaluations per iteration, so its efficiency index is 1.316. Then, computational tests show that the discussed method is better than Newton’s method, and does not have significant differences with Super Halley’s method in terms of error produced.