WIAS Preprint No. 1403, (2009)

Tensor product approximations of high dimensional potentials


  • Lanzara, Flavia
  • Maz'ya, Vladimir
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 41A30 65D15 41A63 41A25


  • Cubature of integral operators, multivariate approximation, tensor product approximation




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.

Appeared in

  • Math. Comp., 80 (2011) pp. 887--904 under the new title Ön the fast computation of high dimensional volume potentials".

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