On the best approximation by ridge functions in the uniform norm

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)61-85
Number of pages25
JournalConstructive Approximation
Volume18
Issue number1
DOIs
StatePublished - 2002

Keywords

  • Ridge functions, Sobolev class, Best approximation

ASJC Scopus subject areas

  • Analysis
  • Mathematics (all)
  • Computational Mathematics

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