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- ItemTensor product approximations of high dimensional potentials(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Lanzara, Flavia; Mazʾya, Vladimir; Schmidt, GuntherThe 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