Approximation complexity of additive random fields

Research output

10 Citations (Scopus)

Abstract

Let X (t, ω) be an additive random field for (t, ω) ∈ [0, 1]d × Ω. We investigate the complexity of finite rank approximationX (t, ω) ≈ underover(∑, k = 1, n) ξk (ω) φ{symbol}k (t) .The results are obtained in the asymptotic setting d → ∞ as suggested by Woźniakowski [Tractability and strong tractability of linear multivariate problems, J. Complexity 10 (1994) 96-128.]; [Tractability for multivariate problems for weighted spaces of functions, in: Approximation and Probability. Banach Center Publications, vol. 72, Warsaw, 2006, pp. 407-427.]. They provide quantitative version of the curse of dimensionality: we show that the number of terms in the series needed to obtain a given relative approximation error depends exponentially on d. More precisely, this dependence is of the form Vd, and we find the explosion coefficient V.

Original languageEnglish
Pages (from-to)362-379
Number of pages18
JournalJournal of Complexity
Volume24
Issue number3
DOIs
Publication statusPublished - 1 Jan 2008

Scopus subject areas

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

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