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Forme confluente de l'ε-algorithme topologique

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Abstract

This paper deals with a confluent form of the topological ε-algorithm which is a method to accelerate the convergence of a sequence of elements of a topological vector space. After giving the rules of the algorithm it is related to some generalizations of the functional Hankel determinants. Some properties and some results about it are proved. An interpretation of the algorithm is given. The last paragraph is devoted with convergence results about the confluent form of the topological ε-algorithm. A parameter is introduced in the algorithm to accelerate the convergence. The optimal value of this parameter is caracterized. By estimating this optimal value, the confluent form of the ϕ-algorithm is obtained. The paper ends with a remark about the confluent form of the topological ϱ-algorithm.

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Références

  1. Brezinski, C.: Généralisations de la transformation de Shanks, de la table de Padé et de l' ε-algorithme. À paraitre dans Calcolo (1975)

  2. Brezinski, C.: Convergence d'une forme confluente de ll'ε-algorithme. C. R. Acad. Sc. Paris,273A, 582–585 (1971)

    Google Scholar 

  3. Brezinski, C.: Méthodes d'accélération de la convergence en analyse numérique thèse. Grenoble 1971

  4. Brezinski, C.: Résultats sur les procédés de sommation et l'ε-algorithme. RIRO, R 3, 147–153 (1970)

    Google Scholar 

  5. Brezinski, C.: Etude sur les ε et ϱ-algorithmes. Numer. Math.17, 153–162 (1971)

    Google Scholar 

  6. Brezinski, C.: Accélération de la convergence en analyse numérique, Publication 41. Laboratoire de Calcul, Université de Lille, 1973

  7. Brezinski, C.: Intégration des systèmes différentiels à l'aide du ϱ-algorithme. C. R. Acad. Sc. Paris,278A, 875–878 (1974)

    Google Scholar 

  8. Ver Eecke, P.: Calcul différentiel. CDU, Paris 1969

    Google Scholar 

  9. Wynn, P.: On a device for computing thee m (S n) transformation. MTAC10, 91–96 (1956)

    Google Scholar 

  10. Wynn, P.: Confluent forms of certain nonlinear algorithms. Arch. Math.11, 223–234 (1960)

    Google Scholar 

  11. Wynn, P.: Upon the definition of an integral as the limit of a continued fraction. Arch. Rat. Mech. Anal.28, 83–148 (1968)

    Google Scholar 

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Authors and Affiliations

  1. U.E.R. d'I.E.E.A. Informatique, BP 36, F-59650, Villeneuve d'Ascq, Françe

    C. Brezinski

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  1. C. Brezinski
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Brezinski, C. Forme confluente de l'ε-algorithme topologique. Numer. Math. 23, 363–370 (1974). https://doi.org/10.1007/BF01438262

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  • DOI: https://doi.org/10.1007/BF01438262

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