Summary
It is well known that some information is needed for accelerating efficiently the convergence of a sequence. We show in this article that, for several families of sequences, there is no algorithm accelerating the convergence of every sequence of the family.
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Références
Brezinski, C.: Accélération de la convergence en analyse numérique. Lecture Notes in Mathematics, Vol. 584. Berlin Heidelberg New York: Springer 1977
Delahaye, J.P.: Quelques problèmes posés par les suites de points non convergentes et algorithmes pour traiter de telles suites. Thèse de 3° cycle — Université de Lille I — 1979
Delahaye, J.P., Germain-Bonne, B.: Quelques résultats négatifs en accélération de la convergence. Pub. ANO 6. Bât. Informatique — 59655 Villeneuve d'Ascq — Cédex — France (1979)
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Delahaye, J.P., Germain-Bonne, B. Résultats négatifs en accélération de la convergence. Numer. Math. 35, 443–457 (1980). https://doi.org/10.1007/BF01399010
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DOI: https://doi.org/10.1007/BF01399010