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 ≤ ∞ behaves asymptotically as n -r/(d-1) . In particular, we obtain this asymptotic estimate for the uniform norm p=q= ∞.
Original language | English |
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Pages (from-to) | 61-85 |
Number of pages | 25 |
Journal | Constructive Approximation |
Volume | 18 |
Issue number | 1 |
DOIs | |
State | Published - 2002 |
Keywords
- Ridge functions, Sobolev class, Best approximation
ASJC Scopus subject areas
- Analysis
- Mathematics (all)
- Computational Mathematics