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)
Vol 6, No 2 (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.