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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…

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

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…