TITLE:
Constructive Theory of Designing Optimal Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations
AUTHORS:
Tugal Zhanlav, Khuder Otgondorj, Renchin-Ochir Mijiddorj
KEYWORDS:
Multipoint Methods, Derivative-Free Methods, Order of Convergence
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.10 No.1,
March
17,
2020
ABSTRACT: This paper stresses the theoretical nature of constructing the optimal derivative-free iterations. We give necessary and sufficient conditions for derivative-free three-point iterations with the eighth-order of convergence. We also establish the connection of derivative-free and derivative presence three-point iterations. The use of the sufficient convergence conditions allows us to design wide class of optimal derivative-free iterations. The proposed family of iterations includes not only existing methods but also new methods with a higher order of convergence.