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Mathematics of Computation

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On tractability of weighted integration over bounded and unbounded regions in $\mathbb{R}^s$

Authors: Fred J. Hickernell, Ian H. Sloan and Grzegorz W. Wasilkowski
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Journal: Math. Comp. 73 (2004), 1885-1901
MSC (2000): Primary 65D05, 65D30, 65Y20, 62M20, 60G25
Published electronically: January 5, 2004
MathSciNet review: 2059741
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Abstract: We prove that for the space of functions with mixed first derivatives bounded in $L_1$ 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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Additional Information

Fred J. Hickernell
Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

Ian H. Sloan
Affiliation: School of Mathematics, University of New South Wales, Sydney 2052, Australia

Grzegorz W. Wasilkowski
Affiliation: Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, Kentucky 40506-0046

Keywords: Weighted integration, quasi--Monte Carlo methods, discrepancy, tractability
Received by editor(s): May 27, 2002
Received by editor(s) in revised form: March 4, 2003
Published electronically: January 5, 2004
Article copyright: © Copyright 2004 American Mathematical Society