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

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

40 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 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
Publication status	Published - Oct 2004
Externally published	Yes

Scopus Subject Areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Discrepancy
quasi-Monte Carlo methods
Tractability
Weighted integration

Access to Document

10.1090/S0025-5718-04-01624-2

Cite this

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title = "On tractability of weighted integration over bounded and unbounded regions in ℝs",

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.",

keywords = "Discrepancy, quasi-Monte Carlo methods, Tractability, Weighted integration",

author = "Hickernell, {Fred J.} and Sloan, {Ian H.} and Wasilkowski, {Grzegorz W.}",

note = "The research was partially supported by the Hong Kong Research Grants Council grant HKBU/2030/99P, the Hong Kong Baptist University Faculty Research Grant FRG/00-01/II-62, the Australian Research Council, and the National Science Foundation under Grant CCR-0095709. ",

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AU - Wasilkowski, Grzegorz W.

N1 - The research was partially supported by the Hong Kong Research Grants Council grant HKBU/2030/99P, the Hong Kong Baptist University Faculty Research Grant FRG/00-01/II-62, the Australian Research Council, and the National Science Foundation under Grant CCR-0095709.

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N2 - 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.

AB - 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.

KW - Discrepancy

KW - quasi-Monte Carlo methods

KW - Tractability

KW - Weighted integration

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