A biparametric family of four-step sixteenth-order root-finding methods with the optimal efficiency index

A biparametric family of four-step multipoint iterative methods of order sixteen to solve nonlinear equations are developed and their convergence properties are established. The optimal efficiency indices are all found to be 1 6 1 / 5 ≈ 1.741101 . Numerical examples as well as comparison with existing methods are demonstrated to verify the developed theory.