An efficient family of weighted-Newton methods with optimal eighth order convergence

Based on Newton’s method, we present a family of three-point iterative methods for solving nonlinear equations. In terms of computational cost, the family requires four function evaluations and has convergence order eight. Therefore, it is optimal in the sense of Kung–Traub hypothesis and has the efficiency index 1.682 which is better than that of Newton’s and many other higher order methods. Some numerical examples are considered to check the performance and to verify the theoretical results. Computational results confirm the efficient and robust character of presented algorithms.