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管秩才能计算张量奇异值分解。本文提出一种新的固定精度随机算法，该算法对于给定的三阶张量和预设的近似误差界，能自动找到最优管秩及对应的低管秩近似。该算法基于随机投影技术，并辅以幂迭代方法以实现更高精度。我们在合成数据集和真实数据集上进行了模拟实验，以展示所提算法的效率和性能。