Local convergence of general Steffensen type methods

Ion Păvăloiu
(original), paper

Abstract

We study the local convergence of a generalized Steffensen method. We show that this method substantially improves the convergence order of the classical Steffensen method. The convergence order of our method is greater or equal to the number of the controlled nodes used in the Lagrange-type inverse interpolation, which, in its turn, is substantially higher than the convergence orders of the Lagrange type inverse interpolation with uncontrolled nodes (since their convergence order is at most (2)).

Author

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Keywords

nonlinear equations in R; Steffensen method.

PDF

PDF-LaTeX file (on the journal website).

Cite this paper as:

I. Păvăloiu, Local convergence of general Steffensen type methods, Rev. Anal. Numér. Théor. Approx., 33 (2004) 1, pp. 79-86.

About this paper

Journal

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

Publisher Name

Editions de l’Academie Roumaine

Article on the journal website

https://ictp.acad.ro/jnaat/journal/article/view/2004-vol33-no1-art10

Print ISSN

1222-9024

Online ISSN

2457-8126

References

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2004

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