A family of modified Ostrowski’s methods with optimal eighth order of convergence

In this paper, we derive a new family of eighth-order methods for obtaining simple roots of nonlinear equations by using the weight function method. Each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices are 1.682, which are optimal according to the Kung and Traub’s conjecture (1974) [2]. Numerical comparisons are made to show the performance of the derived method, as is shown in the numerical section.