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Abstract It is well known that the Steffensen and Aitken-Steffensen type methods are obtained from the chord method, using controlled…

Abstract In this paper we deal with iterative methods of interpolatory type, for solving nonlinear equations in Banach spaces. We…

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…

Abstract We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence…

Abstract In this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods.…

Abstract We provide sufficient conditions for the convergence of the Steffensen method for solving the scalar equation \(f(x)=0\), without assuming…

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

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