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.