Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension

@article{Khoromskij2010FastAA,
  title={Fast and accurate tensor approximation of a multivariate convolution with linear scaling in dimension},
  author={Boris N. Khoromskij},
  journal={J. Computational Applied Mathematics},
  year={2010},
  volume={234},
  pages={3122-3139}
}
In the present paper we present the tensor-product approximation of multidimensional convolution transform discretized via collocation-projection scheme on the uniform or composite refined grids. Examples of convolving kernels are given by the classical Newton, Slater (exponential) and Yukawa potentials, 1/‖x‖, e−λ‖x‖ and e−λ‖x‖/‖x‖ with x ∈ Rd. For piecewise constant elements on the uniform grid of size nd, we prove the quadratic convergence O(h2) in the mesh parameter h = 1/n, and then… CONTINUE READING