Matthies, G., Salimi, M., Sharifi, S. and Varona, J.L. (2016) An Optimal Three-Point Eighth-Order Iterative Method without Memory for Solving Nonlinear Equations with Its Dynamics. Japan Journal of Industrial and Applied Mathematics, 33, 751-766.
https://doi.org/10.1007/s13160-016-0229-5

has been cited by the following article:

• 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.