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：本文旨在开发两种基于tubal乘积（t-乘积）的快速随机算法，用于计算广义张量奇异值分解（GTSVD）。利用随机投影方法计算底层数据张量的重要作用，并以此获取原始数据张量的小规模草图，便于后续处理。由于草图张量尺寸较小，可对其应用确定性方法计算GTSVD。随后，从小规模草图张量的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。