Optimal derivative-free root finding methods based on the Hermite interpolation

Abstract

We develop n-point optimal derivative-free root finding methods of order 2n, based on the Hermite interpolation, by applying a first-order derivative transformation. Analysis of convergence confirms that the optimal order of convergence of the transformed methods is preserved, according to the conjecture of Kung and Traub. To check the effectiveness and reliability of the newly presented methods, different type of nonlinear functions are taken and compared.