The existing randomized algorithms need an initial estimation of the tubal rank to compute a tensor singular value decomposition. This paper proposes a new randomized fixedprecision algorithm which for a given third-order tensor and a prescribed approximation error bound, automatically finds an optimal tubal rank and the corresponding low tubal rank approximation. The algorithm is based on the random projection technique and equipped with the power iteration method for achieving a better accuracy. We conduct simulations on synthetic and real-world datasets to show the efficiency and performance of the proposed algorithm.

翻译：现有的随机算法需要对管秩做一个初步估计才能进行张量奇异值分解。本文提出了一种新的随机定精度算法，针对给定的三阶张量和规定的近似误差界，自动发现最优的管秩和相应的低管秩逼近。该算法基于随机投影技术，配备了幂迭代方法以实现更好的精度。我们在合成和实际数据集上进行模拟，以展示所提出算法的效率和性能。