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

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.