An Efficient Randomized Fixed-Precision Algorithm for Tensor Singular Value Decomposition

The existing randomized algorithms need an initial estimation of the tubal rank to compute a tensor singular value decomposition. This paper proposes a new randomized fixed-precision algorithm which for a given 3rd-order tensor and a prescribed approximation error bound, it automatically finds the tubal rank, and the corresponding low tubal rank approximation. The algorithm is based on the random projection technique and equipped with the power iteration method for achieving a better accuracy. We conduct simulations on the synthetic and real-world datasets to show the efficiency and performance of the proposed algorithm.