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Amat, S., Busquier, S. and Plaza, S. (2004) Dynamics of a Family of Third-Order Iterative Methods That Do Not Require Using Second Derivatives. Applied Mathematics and Computation, 154, 735-746.
https://doi.org/10.1016/S0096-3003(03)00747-1

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.