Computation of a tensor singular value decomposition (t-SVD) with a few number of passes over the underlying data tensor is crucial in using modern computer architectures, where the main concern is the communication cost. The current subspace randomized algorithms for computation of the t-SVD, need 2q + 2 number of passes over the data tensor where q is a non-negative integer number (power iteration parameter). In this paper, we propose a new and flexible randomized algorithm which works for any number of passes q, not necessarily being an even number. It is a generalization of the methods developed for matrices to tensors. The expected error bound of the proposed algorithm is derived. Several numerical experiments are conducted and the results confirmed that the proposed algorithm is efficient and applicable. We also use our proposed method to develop a fast algorithm for tensor completion problem.

翻译：光量单值分解(t- SVD) 的计算, 包括几处数据分解, 对使用现代计算机结构至关重要, 其中主要关注的是通信成本。 目前用于计算 t- SVD 的子空间随机算法, 需要 2q + 2 乘以数据分解数, q 是非负整数( 动力迭代参数 ) 。 在本文中, 我们提议一种新的灵活随机算法, 适用于任何数的分解 q, 不一定是一个偶数 。 这是为 Exors 开发的矩阵方法的概括化 。 所拟议的算法的预期误差被推算出来。 进行了数性实验, 结果确认, 提议的算法是有效和适用的 。 我们还使用我们建议的方法, 开发一个快速算法, 解决 Exor 完成问题 。