|
|||||
|
|
On the Best Approximation by Ridge Functions in the Uniform Norm |
|
| Authors: | Y. Gordon V. Maiorov M. Meyer S. Reisner |
| Affiliation: | 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. |
| 本文献已被 SpringerLink 等数据库收录！ | |