Modified Ostrowski’s method with eighth-order convergence and high efficiency index

In this paper, based on Newton’s method, we derive a modified Ostrowski’s method with an eighth-order convergence for solving the simple roots of nonlinear equations by Hermite interpolation methods. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency index of the developed method is 1.682, which is optimal according to Kung and Traub’s conjecture Kung and Traub (1974) [2]. Numerical comparisons are made to show the performance of the derived method, as shown in the illustrative examples.