On the convergence order of the iterative methods

Abstract

We study the connection between the convergence order of two sequences. We show that the exist sequences that do not have exact convergence order.

We apply the obtained results to the study of the convergence order of the iterative methods.

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Title

Original title (in French)

Sur l’ordre de convergence des méthodes d’itération

English translation of the title

On the convergence order of the iterative methods

Keywords

convergence order; nonlinear equation; iterative method

References

[1] Brezinski, C., Comparation de suites convergentes, Revue francaise d’informatique et de recherches operationnelles, Nr. R-2, 95–99, (1971).

[2] Pavaloiu, I., Introducere în teoria aproximarii solutiilor ecuatiilor, Editura Dacia, Cluj-Napoca, (1976).

[3] Pavaloiu, I., Sur les procedes iteratifs a un ordre eleve de convergence, Mathematica, Cluj, 12(35), 2 309–324, (1970).

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Cite this paper as:

I. Păvăloiu, Sur l’ordre de convergence des méthodes d’itération, Mathématica, 23(46) (1981) no. 1, pp. 261-272 (in French).

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Mathematica

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Notes

For a full description of this topic in results obtained at ICTP, please consult
A survey on the high convergence orders and computational convergence orders of sequences

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