An Efficient Algorithm for Computing the Approximate t-URV and its Applications

Maolin Che, Yimin Wei

Abstract: This paper is devoted to the definition and computation of the tensor complete orthgonal decomposition of a third-order tensor called t-URV decompositions. We first give the definition for the t-URV decomposition of a third-order tensor and derive a deterministic algorithm for computing the t-URV. We then present a randomized algorithm to approximate t-URV, named compressed randomized t-URV (cort-URV). Note that t-URV and cort-URV are extensions of URV and compressed randomized URV from the matrix case to the tensor case, respectively. We also establish the deterministic and average-case error bounds for this algorithm. Finally, we illustrate the effectiveness of the proposed algorithm via several numerical examples, and we apply cort-URV to compress the data tensors from some image and video databases.