Two-sided randomized algorithms for approximate K-term t-SVD

This paper is devoted to the computation of the approximate K-term t-SVD of third-order tensors via random techniques. With a given truncated term K, we obtain the two-side randomized algorithms for the approximate K-term t-SVD, denoted by two-sided randomized t-SVD. Furthermore, we delve into the deterministic and probabilistic error bounds, considering specific presumptions regarding the proposed algorithm. Additionally, we integrate the current algorithm with the power method to enhance the precision of the approximate K-term t-SVD. To demonstrate the effectiveness of our proposed algorithm, we present several numerical examples.