Multivariate integration inC∞([0,1]d) is not strongly tractable

  • Authors:

  • Jakub Onufry Wojtaszczyk

  • Affiliations:

  • Department of Mathematics, Information and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

  • Venue:
  • Journal of Complexity
  • Year:
  • 2003

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Abstract

It has long been known that the multivariate integration problem for the unit ball in Cr ([0,1]d) is intractable for fixed finite r. H. Wozniakowski has recently conjectured that this is true even if r= ∞. This paper establishes a partial result in this direction. We prove that multivariate integration for infinitely differential functions is not strongly tractable.