## 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…

## 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…

## A note on inexact secant methods

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

## On an Aitken type method

Abstract In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear…

# local convergence

assuming a solution exists, one gives conditions such that iterates chosen sufficiently close to that solution converge to that solution.