Parallel cross interpolation for high-precision calculation of high-dimensional integrals

We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte Carlo, the samples calculated by our algorithm are neither random nor form a regular lattice. Instead we calculate the given function along individual dimensions (modes) and use these values to reconstruct its behaviour in the whole domain. The positions of the calculated univariate fibres are chosen adaptively for the given function. The required evaluations can be executed in parallel along each mode (variable) and over all modes.