Tensor product approximations of high dimensional potentials

Flavia Lanzara; Vladimir Maz'ya; Gunther Schmidt

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arXiv · 0902.2054

Tensor product approximations of high dimensional potentials

Flavia Lanzara·Vladimir Maz'ya·Gunther Schmidt

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Abstract

The paper is devoted to the efficient computation of high-order cubature formulas for volume potentials obtained within the framework of approximate approximations. We combine this approach with modern methods of structured tensor product approximations. Instead of performing high-dimensional discrete convolutions the cubature of the potentials can be reduced to a certain number of one-dimensional convolutions leading to a considerable reduction of computing resources. We propose one-dimensional integral representions of high-order cubature formulas for n-dimensional harmonic and Yukawa potentials, which allow low rank tensor product approximations.

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Flavia Lanzara, Vladimir Maz'ya, Gunther Schmidt. 2009-02-12. Tensor product approximations of high dimensional potentials. https://arxiv.org/abs/0902.2054

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