MODIFIED HOUSEHOLDER METHOD OF FIFTH ORDER OF CONVERGENCE AND ITS DYNAMICS ON COMPLEX PLANE - Putri, Ayunda; Imran, M; Marjulisa, Rike (Journal of Fundamental Mathematics and Applications (JFMA), 2023)
In this paper, a modified Householder method of fifth order is proposed for solving nonlinear equations. The modification is done by adapting a cubic interpolation polynomial to approximate the second derivative in the Householder method. Weprovide a theorem to prove the order of convergence of the proposed method. The simulations reveal that the proposed method needs fewer iterations, even with challenging initial guesses, and excels in sending a large portion of initial points to convergence and exhibits rapid convergence.