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…
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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…
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 The inverse interpolatory polynomials of Hermite type with 2 nodes, allhaving the same order of multiplicity \(q\in N\), provide…