Open problems for tractability of multivariate integration

Authors:
Henryk Woźniakowski
Affiliations:
Department of Computer Science, Columbia University, New York, NY and Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
Venue:
Journal of Complexity
Year:
2003

Citing 8
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Abstract

We present a number of open problems regarding the tractability of multivariate integration for various spaces of functions in the worst case and randomized settings. In the worst case setting, we discuss two spaces. The first is a space of infinitely differentiable functions for which the tractability of multivariate integration is open. The second is a weighted tensor product Sobolev space for which necessary and sufficient conditions for tractability of multivariate integration are known. For this space, the exact value of the exponent of strong tractability is unknown, and determining this exponent is open. We end this note by presenting an open problem for the tractability of mtiltivariate integration in the randomized setting.