Etude de l'algorithme de Rémès en l'absence de condition de Haar |
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Authors: | Carasso Claude |
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Institution: | (1) Mathématiques Appliquées; I.R.M.A., Université Scientifique et Médicale de Grenoble, Boîte Postale 53, Centre de Tri, 38041 Grenoble-Cédex, France |
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Abstract: | Summary Using a geometric interpretation, the unicity of a best approximation and the convergence of the Remes-algorithm without the Haar-condition are investigated (in the case of the Tchebycheff-approximation of a continuous function by a linear combination of two continuous functions). Replacing the Haar-condition by a weaker one which is generally satisfied, one obtains a convergence theorem that is weaker than the classical convergence theorem but is sufficient for the applicatons. A generalization of these results is indicated. |
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