## On some Aitken-Steffensen-Halley-type method for approximating the roots of scalar equations

Abstract We extend the Aitken-Steffensen method to the Halley transformation. Under some rather simple assumptions we obtain error bounds for…

## Aitken-Steffensen-type methods for nonsmooth functions (II)

Abstract We present some new conditions which assure that the Aitken-Steffensen method yields bilateral approximation for the solution of a…

## Aitken-Steffensen-type methods for nonsmooth functions (I)

Abstract We study the convergence of the Aitken-Steffensen method for solving a scalar equation $$f(x)=0$$. Under reasonable conditions (without assuming…

## On a Halley-Steffensen method for approximating the solutions of scalar equations

Abstract We show that the Steffensen method for solving the scalar equation $$f(x)=0$$, applied to equation $$h(x)=\frac{f(x)}{\sqrt{f'(x)}}=0$$, leads to bilateral…

## Optimal efficiency index of a class of Hermite iterative methods with two steps

Abstract (soon) AuthorsIon Păvăloiu Keywords(soon) References[1] BRENT, R., WINOGRAD, S., WOLFE, F., Optimal Iterative Processes for Root-Finding, Numer. Math., 20,…