On a Steffensen-Hermite type method for approximating the solutions of nonlinear equations
Abstract It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled…
(original)
Accelerating the convergence of the iterative methods of interpolatory type
Abstract In this paper we deal with iterative methods of interpolatory type, for solving nonlinear equations in Banach spaces. We…
Local convergence of some Newton type methods for nonlinear systems
Abstract In order to approximate the solutions of nonlinear systems \[F(x)=0,\] with \(F:D\subseteq {\mathbb R}^n \rightarrow {\mathbb R}^n\), \(n\in {\mathbb…
Local convergence of general Steffensen type methods
Abstract We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence…
On the convergence order of some Aitken-Steffensen type methods
Abstract In this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods.…
On a third order iterative method for solving polynomial operator equations
Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).…
Aitken-Steffensen-type methods for nonsmooth functions (III)
Abstract We provide sufficient conditions for the convergence of the Steffensen method for solving the scalar equation \(f(x)=0\), without assuming…
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…