Randomized algorithms for the computation of multilinear rank-(μ1,μ2,μ3) approximations

We present some randomized algorithms for computing multilinear rank-(mu(1),mu(2),mu(3)) approximations of tensors by combining the sparse subspace embedding and the singular value decomposition. The error bound for this algorithm with the high probability is obtained by the properties of sparse subspace embedding. Furthermore, combining the power scheme and the proposed randomized algorithm, we derive a three-stage randomized algorithm and make a probabilistic analysis for its error bound. The efficiency of the proposed algorithms is illustrated via numerical examples.