On a robust Aitken-Newton method based on the Hermite polynomial

Abstract We introduce an Aitken–Newton iterative method for nonlinear equations, which is obtained by using the Hermite inverse interpolation polynomial…

Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three

Abstract We study the local convergence of some Aitken–Steffensen–Hermite type methods of order three. We obtain that under some reasonable…

A unified treatment of the modified Newton and chord methods

Abstract The aim of this paper is to obtain a unified treatment of some iterative methods. We obtain some conditions…

On a Steffensen-Hermite method of order three

Abstract In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the…

On a Steffensen type method

Abstract We study a general Steffensen type method based on the inverse interpolation Lagrange polynomial of second degree. We show…

On the Chebyshev method for approximating the eigenvalues of linear operators

Abstract We study the approximation of an eigenpair (an eigenvalue and a corresponding eigenvector) of a a linear operator T from…

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…

Remarks on some Newton and Chebyshev-type methods for approximation eigenvalues and eigenvectors of matrices

Abstract We consider a square matrix $$A$$ with real or complex elements. We denote $$\mathbb{K}=\mathbb{R}$$ or $$\mathbb{C}$$ and we are…