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

Fred J. Hickernell; Ian H. Sloan; Grzegorz W. Wasilkowski

doi:10.1090/S0025-5718-04-01624-2

On tractability of weighted integration over bounded and unbounded regions in ℝ^s

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

Computer Science

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

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 language	English
Pages (from-to)	1885-1901
Number of pages	17
Journal	Mathematics of Computation
Volume	73
Issue number	248
DOIs	https://doi.org/10.1090/S0025-5718-04-01624-2
State	Published - Oct 2004

Keywords

Discrepancy
Tractability
Weighted integration
quasi-Monte Carlo methods

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

Access to Document

10.1090/S0025-5718-04-01624-2

Cite this

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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.",

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KW - quasi-Monte Carlo methods

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