On the convergence order of some Aitken-Steffensen type methods

Ion Păvăloiu

doi:10.33993/jnaat322-748

Authors

Ion Păvăloiu Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat322-748

Keywords:

Steffensen, Aitken and Aitken-Steffensen iterations

Abstract views: 254

Abstract

In this note we make a comparative study of the convergence orders for the Steffensen, Aitken and Aitken-Steffensen methods. We provide some conditions ensuring their local convergence. We study the case when the auxiliary operators used have convergence orders \(r_{1},r_{2}\in \mathbb{N}\) respectively. We show that the Steffensen, Aitken and Aitken-Steffensen methods have the convergence orders \(r_{1}+1\), \(r_{1}+r_{2}\) and \(r_{1}r_{2}+r_{1}\) respectively.

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