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Cordero, A., Hueso, J.L., Martinez, E. and Torregrosa, J.R. (2013) A New Technique to Obtain Derivative-Free Optimal Iterative Methods for Solving Nonlinear Equations. The Journal of Computational and Applied Mathematics, 252, 95-102.
https://doi.org/10.1016/j.cam.2012.03.030

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.