High-Order Derivative-Free Newton-Type Iterations

A unified approach to the construction of higher-order two- and three-step derivative-free iterations for solving a system of nonlinear equations is introduced. As in Chap.  5 , the necessary and sufficient convergence conditions are written in terms of parameters. The two parametric families of derivative-free iterations include some well-known methods as particular cases. We also discuss the computational cost of the considered methods and select the most efficient and cheapest methods.