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We derive new formulas for the high dimensional biharmonic potential actingon Gaussians or Gaussians times special polynomials. These formulas can be usedto construct accurate cubature formulas of an arbitrary high order which arefast and effective also in very high dimensions. Numerical tests show that theformulas are accurate and provide the predicted approximation rate (O(h^8)) upto the dimension 10^7.

Fast cubature of high dimensional biharmonic potential based on Approximate Approximations