A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function

A biparametric family of four-step multipoint iterative methods of order sixteen to numerically solve nonlinear equations are developed and their convergence properties are investigated. The efficiency indices of these methods are all found to be 16^1/5≈1.741101, being optimally consistent with the conjecture of Kung-Traub. Numerical examples as well as comparison with existing methods developed by Kung-Traub and Neta are demonstrated to confirm the developed theory in this paper.