Skip to Main content Skip to Navigation
Journal articles

On the best approximation by ridge functions in the uniform norm

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 less than or equal to q less than or equal to p less than or equal to infinity behaves asymptotically as n(-r/(d-1)). In particular, we obtain this asymptotic estimate for the uniform norm p = q = infinity.
Document type :
Journal articles
Complete list of metadatas

https://hal-upec-upem.archives-ouvertes.fr/hal-00693663
Contributor : Admin Lama <>
Submitted on : Wednesday, May 2, 2012 - 10:03:27 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

Identifiers

  • HAL Id : hal-00693663, version 1

Citation

Y Gordon, V Maiorov, Mathieu Meyer, S Reisner. On the best approximation by ridge functions in the uniform norm. Constructive Approximation, Springer Verlag, 2002, 18 (1), pp.61--85. ⟨hal-00693663⟩

Share

Metrics

Record views

452