Abstract

In this note we study the convergence of a generalized Aitken type method for approximating the solutions of nonlinear equations in R. We obtain conditions which assure monotone convergence of the generated sequences. We also obtain a posteriori estimations for the errors.

Author

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis)

Keywords

nonlinear equations in R; Aitken method

Cite this paper as:

I. Păvăloiu, E. Cătinaş, On an Aitken type method, Rev. Anal. Numér. Théor. Approx., 36 (2007) no. 2, pp. 173-176.

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About this paper

Print ISSN

1222-9024

Online ISSN

2457-8126

MR

1222-9024

Online ISSN

2457-8126

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References

[1] M.A. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York and London, 1980.
[2] I. Pavaloiu, Solutions Equations by Interpolation, Dacia, Cluj-Napoca, 1981 (in Romanian).
[3] I. Pavaloiu, Bilateral approximation of solution of equations by order three Steffensen-type methods , Studia Univ. “Babes-Bolyai”, Mathematica, LI (2006) no. 3, pp. 105–114.
[4] I. Pavaloiu and N. Pop, Interpolation and Applications, Risoprint, Cluj-Napoca, 2005 (in Romanian).
[5] I. Pavaloiu, Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences , Calcolo, 32 (1995) nos. 1–2, pp. 69–82.
[6] I. Pavaloiu and E. Catinas, On a Steffensen type method, Proceedings of the Ninth International Symposion on Symbolic and Numeric Algoritms for Scientific Computing (SYNASC 2007), September 26–29, 2007, Timisoara, Romania, IEEE Computer Society, pp. 369–375.
[7] B.A. Turowicz, Sur les derivees d’ordre superieur d’une fonction inverse , Ann. Polon. Math., 8 (1960), pp. 265–269.

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