On the necessity of low-effective dimension

Authors:
Shu Tezuka
Affiliations:
Faculty of Mathematics, Kyushu University, Higashi-ku, Fukuoka-shi, Fukuoka-ken, Japan
Venue:
Journal of Complexity
Year:
2005

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Abstract

We introduce a class of functions in high dimensions which have the maximum effective dimension, then prove that generalized Sobol' sequences provide the O(N-1) convergence rate for the integration of this class of functions. An important consequence is that high-dimensional problems for which quasi-Monte Carlo outperforms Monte Carlo are not necessarily of low-effective dimension.