Average case optimal algorithms in Hilbert spaces

G. W. Wasilkowski, H. Woźniakowski

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

We study optimal algorithms and optimal information for an average case model. This is done for linear problems in a separable Hilbert space equipped with a probability measure. We show, in particular, that for any measure a (linear) spline algorithm is optimal among linear algorithms. The spline algorithm is defined in terms of the covariance operator of the measure. We provide a condition on the measure which guarantees that the spline algorithm is optimal among all algorithms. The problem of optimal information is also solved.

Original languageEnglish
Pages (from-to)17-25
Number of pages9
JournalJournal of Approximation Theory
Volume47
Issue number1
DOIs
StatePublished - May 1986

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Mathematics (all)
  • Applied Mathematics

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