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预先估计张量奇异值分解中的管秩。本文提出一种新的随机固定精度算法，该算法针对给定的三阶张量和预设的近似误差界，能自动确定最优管秩及相应的低管秩近似。该算法基于随机投影技术，并结合幂迭代方法以提升精度。我们在合成数据集和实际数据集上进行仿真实验，验证了所提算法的有效性和性能。