Can adaption help on the average?

G. W. Wasilkowski, H. Woźniakowski

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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 does not 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.

Original languageEnglish
Pages (from-to)169-190
Number of pages22
JournalNumerische Mathematik
Issue number2
StatePublished - Jun 1984


  • Subject Classifications: AMS(MOS): 68C25, CR: F2.1

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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