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In the present paper we present the tensor-product approximation of multi-dimensional 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,
For piecewise constant elements on the uniform grid of size
The fast algorithm of complexity
Finally, we give numerical illustrations confirming:
(a) the approximation theory for convolution schemes of order
(b) linear-logarithmic scaling of 1D discrete convolution on composite grids;
(c) linear-logarithmic scaling in