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Ukrainian Mathematical Journal

, Volume 62, Issue 3, pp 452–466 | Cite as

Best approximation by ridge functions in L p -spaces

  • V. E. Maiorov
Article

We study the approximation of the classes of functions by the manifold R n formed by all possible linear combinations of n ridge functions of the form r(a · x)): It is proved that, for any 1 ≤ qp ≤ ∞, the deviation of the Sobolev class W r p from the set R n of ridge functions in the space L q (B d ) satisfies the sharp order n -r/(d-1).

Keywords

Orthogonal Polynomial Orthonormal System Orthogonal System Algebraic Polynomial Multivariate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • V. E. Maiorov
    • 1
  1. 1.TechnionHaifaIsrael

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