On tractability of weighted integration over bounded and unbounded regions in ℝs

Fred J. Hickernell*, Ian H. Sloan, Grzegorz W. Wasilkowski

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

39 Citations (Scopus)

Abstract

We prove that for the space of functions with mixed first derivatives bounded in L1 norm, the weighted integration problem over bounded or unbounded regions is equivalent to the corresponding classical integration problem over the unit cube, provided that the integration domain and weight have product forms. This correspondence yields tractability of the general weighted integration problem.

Original languageEnglish
Pages (from-to)1885-1901
Number of pages17
JournalMathematics of Computation
Volume73
Issue number248
DOIs
Publication statusPublished - Oct 2004
Externally publishedYes

Scopus Subject Areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Discrepancy
  • quasi-Monte Carlo methods
  • Tractability
  • Weighted integration

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