Approximation of linear functionals on a banach space with a Gaussian measure

D. Lee, G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


We study approximation of linear functionals on separable Banach spaces equipped with a Gaussian measure. We study optimal information and optimal algorithms in average case, probabilistic, and asymptotic settings, for a general error criterion. We prove that adaptive information is not more powerful than nonadaptive information and that μ-spline algorithms, which are linear, are optimal in all three settings. Some of these results hold for approximation of linear operators. We specialize our results to the space of functions with continuous rth derivatives, equipped with a Wiener measure. In particular, we show that the natural splines of degree 2r + I yield the optimal algorithms. We apply the general results to the problem of integration.

Original languageEnglish
Pages (from-to)12-43
Number of pages32
JournalJournal of Complexity
Issue number1
StatePublished - Mar 1986

Bibliographical note

Funding Information:
*This research was supported in part by the National Science Foundation under Grant DCR-82-14322. ‘Current address: AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, N. J. 07974.

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • General Mathematics
  • Control and Optimization
  • Applied Mathematics


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