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= ∞.
- Ridge functions, Sobolev class, Best approximation
ASJC Scopus subject areas
- General Mathematics
- Computational Mathematics