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Papers published at ICTP.

The papers published by the ICTP members before or after being ICTP members are categorized as not@ictp.

A note on inexact secant methods

Abstract The inexact secant method $$[x_{k-1},x_{k};F]s_{k}=-F(x_k) +r_k$$, $$x_{k+1}=x_k+s_k$$, $$k=1,2,\ldots$$, $$x_0,x_1 \in {\mathbb R}^n$$ is considered for solving the nonlinear…

On some Steffensen-type iterative methods for a class of nonlinear equations

Abstract Consider the nonlinear equations $$H(x):=F(x)+G(x)=0$$, with $$F$$ differentiable and $$G$$ continuous, where $$F,G,H:X \rightarrow X$$ are nonlinear operators and $$X$$…

On some iterative methods for solving nonlinear equations

Abstract Consider the nonlinear equation $$H(x):=F(x)+G(x)=0$$, with $$F$$ differentiable and $$G$$ continuous, where $$F,G,H:X \rightarrow X$$, $$X$$ a Banach space.  The…

On some interpolation iterative methods with optimal convergence speed

Abstract We consider nonlinear equations in $$\mathbb{R}$$, and a class of iterative methods obtained by inverse interpolation of Hermite type.…

On the efficiency of the computations for approximating the solutions of equations

Abstract We consider the iterative methods for solving nonlinear equations in $$\mathbb{R}$$ and the class of iterative methods obtained by…

On some interpolatory iterative methods for the second degree polynomial operators (I)

Abstract In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree…

On an approximation formula

Abstract We generalize an approximation formula which in some particular cases has been studied by [J.F. Traub 1964] and \…

On some interpolatory iterative methods for the second degree polynomial operators (II)

Abstract In this paper we apply some iterative methods obtained by inverse interpolation, in order to solve some specific classes…

Monotone sequences for approximating the solutions of equations

Abstract We study the local convergence of a Aitken-Steffensen type method for approximating the solutions of nonlinear scalar equations. We…

On the convergence order of the iterative methods

Abstract We study the connection between the convergence order of two sequences. We show that the exist sequences that do…