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Efficient and fast computation of a tensor singular value decomposition(t-SVD) with a few passes over the underlying data tensor is crucial because ofits many potential applications. The current/existing subspace randomizedalgorithms need (2q+2) passes over the data tensor to compute a t-SVD, where qis a non-negative integer number (power iteration parameter). In this paper, wepropose an efficient and flexible randomized algorithm that can handle anynumber of passes q, which not necessary need be even. The flexibility of theproposed algorithm in using fewer passes naturally leads to lower computationaland communication costs. This advantage makes it particularly appropriate whenour task calls for several tensor decompositions or when the data tensors arehuge. The proposed algorithm is a generalization of the methods developed formatrices to tensors. The expected/ average error bound of the proposedalgorithm is derived. Extensive numerical experiments on random and real-worlddata sets are conducted, and the proposed algorithm is compared with somebaseline algorithms. The extensive computer simulation experiments demonstratethat the proposed algorithm is practical, efficient, and in general outperformsthe state of the arts algorithms. We also demonstrate how to use the proposedmethod to develop a fast algorithm for the tensor completion problem.

A Randomized Algorithm for Tensor Singular Value Decomposition using an Arbitrary Number of Passes