Open AccessModifikasi Metode Householder Tiga Parameter yang Bebas Turunan Kedua dengan Orde Konvergensi Optimal
Author(s) -
Wartono,
M Zulianti,
Rahmawati Rahmawati
Publication year - 2021
Publication title -
jurnal ilmiah matematika dan terapan/jurnal ilmiah matematika dan terapan
Language(s) - English
Resource type - Journals
eISSN - 2540-766X
pISSN - 1829-8133
DOI - 10.22487/2540766x.2021.v18.i1.15434
Subject(s) - iterative method , convergence (economics) , mathematics , taylor series , nonlinear system , mathematical optimization , function (biology) , order (exchange) , computer science , mathematical analysis , physics , finance , quantum mechanics , evolutionary biology , economics , biology , economic growth
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.