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On the Best Approximation by Ridge Functions in the Uniform Norm |
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| Authors: | Y Gordon V Maiorov M Meyer S Reisner |
| Institution: | Department of Mathematics Technion, I.I.T. Haifa, 32000 Israel gordon@tx.technion.ac.il, IL Department of Mathematics Technion, I.I.T. Haifa, 32000 Israel maiorov@tx.technion.ac.il, IL Equipe d'Analyse et Mathématiques Appliquées Université de Marne-la-Vallée 5 Boulevard Descartes Champs sur Marne 77454 Marne-la-Vallée Cedex 2 France meyer@math.univ-mlv.fr, FR Department of Mathematics University of Haifa Haifa 31905 Israel reisner@mathcs2.haifa.ac.il, IL |
| Abstract: | We consider the best approximation of some function classes by the manifold M n consisting of sums of n arbitrary ridge functions. It is proved that the deviation of the Sobolev class W p r,d from the manifold M n in the space L q for any 2≤ q≤ p≤∈fty behaves asymptotically as n -r/(d-1) . In particular, we obtain this asymptotic estimate for the uniform norm p=q=∈fty . January 10, 2000. Date revised: March 1, 2001. Date accepted: March 12, 2001. |
| Keywords: | , Ridge functions, Sobolev class, Best approximation, AMS Classification, 41A46, 41A50, 42A61, 42C10, |
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