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Generalisations de la transformation de shanks, de la table de Pade et de l'ε-algorithme

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Abstract

This paper deals with a generalization of the Shank's transformation for a sequence of elements of a topological vector space. It is showned how this generalization leads to a generalization of the Padé table. A recursive algorithm for effecting this transformation is given. Its properties are studied and some theorems are proved. This algorithm can be considered as a generalization of the ε-algorithm of Wynn. A second generalization is also studied and a third one which needs less elements of the initial sequence. The paper ends with a discussion on the vector case.

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  1. UER d'IEEA-Informatique, BP 36, 59650, Villeneuve d'Ascq, Françe

    C. Brezinski

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  1. C. Brezinski
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Brezinski, C. Generalisations de la transformation de shanks, de la table de Pade et de l'ε-algorithme. Calcolo 12, 317–360 (1975). https://doi.org/10.1007/BF02575753

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