Liberating the dimension for L2-approximation

G. W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We consider approximation of ∞-variate functions with the error measured in a weighted L2-norm. The functions being approximated belong to weighted tensor product spaces with arbitrary weights γμ. We provide complexity upper bounds and sufficient conditions for polynomial and weak tractabilities expressed in terms of the properties of the weights γμ and the complexity of the corresponding univariate approximation problem. These tractability conditions are also necessary for important types of weights including product weights.

Original languageEnglish
Pages (from-to)304-319
Number of pages16
JournalJournal of Complexity
Volume28
Issue number3
DOIs
StatePublished - Jun 2012

Keywords

  • Approximation
  • Complexity
  • Integration
  • Tractability

ASJC Scopus subject areas

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

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