Comparison of some optimal derivative-free three-point iterations

Abstract

We show that the well-known Khattri et al. methods and Zheng et al. methods are identical. In passing, we propose a suitable calculation formula for Khattri et al. methods. We also show that the families of eighth-order derivative-free methods obtained in [8] include some existing methods, among them the above-mentioned ones as particular cases. We also give the sufficient convergence condition of these families. Numerical examples and comparison with some existing methods were made. In addition, the dynamical behavior of methods of these families is analyzed.