Fast computation of the multidimensional fractional Laplacian

The paper discusses new cubature formulas for the Riesz potential and the fractional Laplacian (Formula presented.), (Formula presented.), in the framework of the method approximate approximations. This approach, combined with separated representations, makes the method successful also in high dimensions. We prove error estimates and report on numerical results illustrating that our formulas are accurate and provide the predicted convergence rate 2, 4, 6, 8 up to dimension (Formula presented.). © 2021 Informa UK Limited, trading as Taylor & Francis Group.