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arXiv · 0803.0441

Multivariate integration in C^\infty([0,1]^d) is not strongly tractable

Jakub Onufry Wojtaszczyk
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Abstract

It has long been known that the multivariate integration problem for the unit ball in $C^r([0,1]^d)$ is intractable for fixed finite $r$. H. Woźniakowski has recently conjectured that this is true even if $r=\infty$. This paper establishes a partial result in this direction. We prove that the multivariate integration problem, for infinitely differential functions all of whose variables are bounded by one, is not strongly tractable.

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Jakub Onufry Wojtaszczyk. 2008-03-04. Multivariate integration in C^\infty([0,1]^d) is not strongly tractable. https://arxiv.org/abs/0803.0441

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