An optimized Steffensen-type iterative method with memory associated with annuity calculation

An iteration scheme in the class of Steffensen-type methods is proposed and extended to achieve the optimized speed for methods with memory. In fact, 100% convergence acceleration is obtained in contrast to its version without memory and without any additional functional evaluations. Improvements of the convergence radii by this technique are illustrated by the dynamic of the iterations. Finally, an application of the proposed scheme in computing annuity in finance is furnished.