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：现有随机化算法需要预先估计管秩以计算张量奇异值分解。本文提出一种新的随机化固定精度算法，该算法针对给定三阶张量与预设近似误差界，可自动确定最优管秩并生成相应的低管秩近似。该算法基于随机投影技术，并融入幂迭代方法以提升精度。我们在合成数据集与真实数据集上开展仿真实验，验证了所提算法的效率与性能。