On the local convergence of a family of two-step iterative methods for solving nonlinear equations

A local convergence analysis for a generalized family of two step Secant-like methods with frozen operator for solving nonlinear equations is presented. Unifying earlier methods such as Secant's, Newton, Chebyshev-like, Steffensen and other new variants the family of iterative schemes is built up, where a profound and clear study of the computational efficiency is also carried out. Numerical examples and an application using multiple precision and a stopping criterion are implemented without using any known root. Finally, a study comparing the order, efficiency and elapsed time of the methods suggested supports the theoretical results claimed.