# On an Aitken-Steffensen-Newton type method

## Abstract

We consider an Aitken-Steffensen type method in which the nodes are controlled by Newton and two-step Newton iterations.

We prove a local convergence result showing the -convergence order 7 of the iterations. Under certain supplementary conditions, we obtain monotone convergence of the iterations, providing an alternative to the usual ball attraction theorems.

Numerical examples show that this method may, in some cases, have larger (possibly sided) convergence domains than other methods with similar convergence orders.

## Authors

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Cite this paper as

I. Păvăloiu, A unified treatment of the modified Newton and chord methods, Carpathian J. Math. 25 (2009) no. 2, pp. 192-196.

## PDF

Scanned paper (soon).

##### Publisher Name

Technical University Cluj-Napoca

1584-2851

1843-4401