On the convergence order of some Aitken-Steffensen type methods

Authors

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

Keywords:

Steffensen, Aitken and Aitken-Steffensen iterations

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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References

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Published

2003-08-01

How to Cite

Păvăloiu, I. (2003). On the convergence order of some Aitken-Steffensen type methods. Rev. Anal. Numér. Théor. Approx., 32(2), 193–202. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2003-vol32-no2-art8

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