Ball comparison between two optimal eight-order methods under weak conditions (Q905065)

A local convergence analysis of two families of optimal eighth-order methods in order to approximate a locally unique solution of a nonlinear equation is presented. In previous studies, the convergence order of these methods was given under hypotheses reaching up to the eighth derivative of the function. In this paper, the applicability of these methods by showing convergence using only the first derivative is expanded. The convergence radii and computable error estimates for these methods using Lipschitz constants are received.