On the best approximation by ridge functions in the uniform norm

Y. Gordon; V. Maiorov; M. Meyer; S. Reisner

doi:10.1007/s00365-001-0009-5

On the best approximation by ridge functions in the uniform norm

Y. Gordon, V. Maiorov, M. Meyer, S. Reisner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	61-85
Number of pages	25
Journal	Constructive Approximation
Volume	18
Issue number	1
DOIs	https://doi.org/10.1007/s00365-001-0009-5
State	Published - 2002

Keywords

Ridge functions, Sobolev class, Best approximation

ASJC Scopus subject areas

Analysis
General Mathematics
Computational Mathematics

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10.1007/s00365-001-0009-5

Cite this

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AU - Meyer, M.

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N2 - 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= ∞.

AB - 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= ∞.

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On the best approximation by ridge functions in the uniform norm

Abstract

Keywords

ASJC Scopus subject areas

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