A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations

摘要

A family of derivative-free methods of seventh-orderconvergence for solving nonlinear equations is suggested. In the proposedmethods, several linear combinations of divided differences are used inorder to get a good estimation of the derivative of the given function atthe different steps of the iteration. The efficiency indices of the members ofthis family are equal to 1.6266. Also, numerical examples are used to showthe performance of the presented methods, on smooth and nonsmoothequations, and to compare with other derivative-free methods, includingsome optimal fourth-order ones, in the sense of Kung-Traub’s conjecture.