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.