## On the high convergence orders of the Newton-GMBACK methods

Abstract GMBACK is a Krylov solver for linear systems in $$\mathbb{R}^n$$. We analyze here the high convergence orders (superlinear convergence)…

## On an Aitken-Newton type method

Abstract We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes…

## On a Newton-Steffensen type method

Abstract In this paper we study the convergence of a Newton-Steffensen type method for solving nonlinear equations in R, introduced by…

## 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…

## Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences

Abstract We study the conditions under which the well-known Aitken-Steffensen method for solving equations leads to monotonic sequences whose terms…

## 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).…