Tensor product approximations of high dimensional potentials
For researchers in scientific computing, it provides a method to reduce computational resources for high-dimensional potential calculations.
The paper develops efficient cubature formulas for high-dimensional volume potentials by combining approximate approximations with tensor product methods, reducing high-dimensional convolutions to one-dimensional ones and achieving low-rank tensor approximations.
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.