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Chicharro, F., Cordero, A., Gutirrez, J.M. and Torregrosa, J.R. (2013) Complex Dynamics of Derivative-Free Methods for Nonlinear Equations. Applied Mathematics and Computation, 219, 7023-7035.
https://doi.org/10.1016/j.amc.2012.12.075

has been cited by the following article:

• TITLE: Two Families of Multipoint Root-Solvers Using Inverse Interpolation with Memory

  AUTHORS: Zhongli Liu, Quan Zheng

  KEYWORDS: Nonlinear Equation, General Multipoint Iteration, Inverse Interpolation, Order of Convergence, Basin of Attraction

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.3, March 28, 2023

  ABSTRACT: In this paper, a general family of derivative-free n + 1-point iterative methods using n + 1 evaluations of the function and a general family of n-point iterative methods using n evaluations of the function and only one evaluation of its derivative are constructed by the inverse interpolation with the memory on the previous step for solving the simple root of a nonlinear equation. The order and order of convergence of them are proved respectively. Finally, the proposed methods and the basins of attraction are demonstrated by the numerical examples.