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：本研究致力于开发两种基于管积（t-积）的广义张量奇异值分解（GTSVD）快速随机算法。通过随机投影方法计算底层数据张量的关键作用量，并利用这些作用量获得原始数据张量的小型草图表示，从而降低计算复杂度。由于草图张量规模较小，可采用确定性方法直接计算其GTSVD。随后通过小型草图张量的GTSVD重构原始大规模数据张量的GTSVD。实验结果表明所提方法具有显著效能。