Randomized algorithms for the low multilinear rank approximations of tensors
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In this paper, we develop efficient methods for the computation of low multilinear rank approximations of tensors based on randomized algorithms. Combining the random projection with the singular value decomposition, the rank-revealing QR decomposition and the rank-revealing LU factorization, respectively, we obtain three randomized algorithms for computing the low multilinear rank approximations. Based on the singular values of sub-Gaussian matrices, we derive the error bounds for each algorithm with probability. We illustrate the proposed algorithms via several numerical examples.
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