Parallel Algorithms for Computing the Tensor-Train Decomposition

The tensor-train (TT) decomposition expresses a tensor in data-sparse format used molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT from various inputs: (1) Parallel-TTSVD for traditional format, (2) PSTT its variants streaming data, (3) Tucker2TT Tucker (4) TT-fADI solutions of Sylvester equations. We provide theoretical guarantees accuracy, parallelization methods, scaling analysis, numerical results. For example, -dimension , two-sided sketching algorithm PSTT2 is shown to have memory complexity improving upon previous algorithms.