Exact cubature for a class of functions of maximum effective dimension

Authors:
Shu Tezuka;Anargyros Papageorgiou
Affiliations:
Faculty of Mathematics, Kyushu University, Higashi-ku, Fukuoka-shi, Fukuoka-ken, Japan;Department of Computer Science, Columbia University, New York, NY
Venue:
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
Year:
2006

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Abstract

We consider high-dimensional integration in a broad class of functions where all elements have maximum effective dimension. We show that there exists an exact cubature with only two points. Therefore, not only the convergence but also the worst case error of quasi-Monte Carlo need not depend on the effective dimension at all.