

Preprint 139/2006
Tensor-Product Approximation to Operators and Functions in High Dimensions
Boris N. Khoromskij and Wolfgang Hackbusch
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Submission date: 28. Nov. 2006 (revised version: March 2007)
Pages: 17
published in: Journal of complexity, 23 (2007) 4/6, p. 697-714
DOI number (of the published article): 10.1016/j.jco.2007.03.007
Bibtex
MSC-Numbers: 65F50, 65F30, 46B28, 47A80
Keywords and phrases: Tensor product approximation
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Abstract:
In recent papers tensor-product structured Nyström and Galerkin type
approximations of certain multi-dimensional integral operators have been
introduced and analysed. In the present paper we focus on the analysis of the
collocation type schemes with respect to the tensor-product basis in a high
spatial dimension d. Approximations up to an accuracy are proven to have the storage complexity
with q independent of d, where N is the discrete
problem size. In particular, we apply the theory to a collocation
discretisation of the Newton potential with the kernel
,
,
. Numerical illustrations are given in the
case of d=3.