On the convergence order of the iterative methods

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.

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

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

convergence order; nonlinear equation; iterative method

Scanned paper.

PDF-Latex version of the paper.

For a full description of this topic in results obtained at ICTP, please consult the list of papers on this topic
https://ictp.acad.ro/category/numerical-analysis/convergence-orders/
as well as the recent papers
How many steps still left to x*?, SIAM Review, 2021
A survey on the high convergence orders and computational convergence orders of sequences, Appl. Math. Comput., 2019

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

Google Scholar citations

[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).