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On tractability of weighted integration over bounded and unbounded regions in 
Author(s):
Fred
J.
Hickernell;
Ian
H.
Sloan;
Grzegorz
W.
Wasilkowski.
Journal:
Math. Comp.
73
(2004),
1885-1901.
MSC (2000):
Primary 65D05, 65D30, 65Y20, 62M20, 60G25
Posted:
January 5, 2004
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Abstract:
We prove that for the space of functions with mixed first derivatives bounded in  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
Email:
fred@math.hkbu.edu.hk
Ian
H.
Sloan
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia
Email:
sloan@maths.unsw.edu.au
Grzegorz
W.
Wasilkowski
Affiliation:
Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, Kentucky 40506-0046
Email:
greg@cs.uky.edu
DOI:
10.1090/S0025-5718-04-01624-2
PII:
S 0025-5718(04)01624-2
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
Posted:
January 5, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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