On the convergence order of some Aitken-Steffensen type methods

Ion Păvăloiu
(original), paper

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 \(r_1r_2+r_1\) respectively.

Author

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Keywords

nonlinear equations in R; Steffensen, Aitken and Aitken-Steffensen methods.

PDF

PDF-LaTeX file (on the journal website).

Cite this paper as:

I. Păvăloiu, On the convergence order of some Aitken-Steffensen type methods, Rev. Anal. Numér. Théor. Approx., 32(2003) no. 2, pp. 193-202. https://doi.org/10.33993/jnaat322-748

About this paper

Journal

Revue d’Analyse Numérique et de Théorie de l’Approximation

Publisher Name

Editions de l’Academie Roumaine

DOI

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

Print ISSN

1222-9024

Online ISSN

2457-8126

References

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2003

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