Numerische Mathematik

, Volume 44, Issue 2, pp 169–190

Can adaption help on the average?

  • G. W. Wasilkowski
  • H. Woźniakowski
Article

DOI: 10.1007/BF01410103

Cite this article as:
Wasilkowski, G.W. & Woźniakowski, H. Numer. Math. (1984) 44: 169. doi:10.1007/BF01410103

Summary

We study adaptive information for approximation of linear problems in a separable Hilbert space equipped with a probability measure μ. It is known that adaption does not help in the worst case for linear problems. We prove that adaption also doesnot help on the average. That is, there exists nonadaptive information which is as powerful as adaptive information. This result holds for “orthogonally invariant” measures. We provide necessary and sufficient conditions for a measure to be orthogonally invariant. Examples of orthogonally invariant measures include Gaussian measures and, in the finite dimensional case, weighted Lebesgue measures.

Subject Classifications

AMS(MOS): 68C25 CR: F2.1 

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • G. W. Wasilkowski
    • 1
    • 2
  • H. Woźniakowski
    • 1
    • 2
  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland
  2. 2.Department of Computer ScienceColumbia UniversityNew YorkUSA

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