Derivative-Free Iterative Methods

Necessary and sufficient conditions for derivative-free two- and three-point iterations are obtained. In particular, we propose the finite-difference versions of well-known optimal fourth-order methods. We applied the generating function method for constructing new derivative-free methods and made the comparison of methods based on the dynamical behaviour. Two new parametric sixth- and seventh-order iterative methods with memory are presented, and the optimal values of additional parameters that increase the convergence order are found.