This work deals with developing two fast randomized algorithms for computing the generalized tensor singular value decomposition (GTSVD) based on the tubal product (t-product). The random projection method is utilized to compute the important actions of the underlying data tensors and use them to get small sketches of the original data tensors, which are easier to be handled. Due to the small size of the sketch tensors, deterministic approaches are applied to them to compute their GTSVDs. Then, from the GTSVD of the small sketch tensors, the GTSVD of the original large-scale data tensors is recovered. Some experiments are conducted to show the effectiveness of the proposed approach.

翻译：本文研究基于管积（t-product）的广义张量奇异值分解（GTSVD）的两种快速随机算法。采用随机投影方法计算原始数据张量的关键作用，并利用这些作用获取原始数据张量的小型草图，从而更易于处理。由于草图张量规模较小，可对其应用确定性方法来计算其GTSVD。随后，从小型草图张量的GTSVD中恢复原始大规模数据张量的GTSVD。通过一系列实验验证了所提方法的有效性。