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We develop efficient data-sparse representations to a class of high order tensors via a block many-fold Kronecker product decomposition. Such a decomposition is based on low separation-rank approximations of the corresponding multivariate generating function. We combine the Sinc interpolation and a quadrature-based approximation with hierarchically organised block tensor-product formats. Different matrix and tensor operations in the generalised Kronecker tensor-product format including the Hadamard-type product can be implemented with the low cost. An application to the collision integral from the deterministic Boltzmann equation leads to an asymptotical cost O(n 4 log β n ) - O(n 5 log β n ) in the one-dimensional problem size n (depending on the model kernel function), which noticeably improves the complexity O(n 6 log β n) of the full matrix representation.

Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation