Modifikasi Metode Householder Tiga Parameter yang Bebas Turunan Kedua dengan Orde Konvergensi Optimal

Abstract

The Householder’s method is one of the iterative methods with a third-order convergence that used to solve a nonlinear equation. In this paper, the authors modified the iterative method using the expansion of second order Taylor’s series and approximated its second derivative using equality of two the third-order iterative methods. Based on the results of the study, it was found that the new iterative method has a fourth-order of convergence and requires three evaluations of function with an efficiency index of 1,587401. Numerical simulation is given by using several functions to compare the performance between the new method with other iterative methods. The results of numerical simulation show that the performance of the new method is better than other iterative methods.