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先对管秩进行初始估计才能计算张量奇异值分解。本文提出了一种新的随机固定精度算法，该算法针对给定三阶张量和预设的近似误差界，可自动找到最优管秩及相应的低管秩近似。该算法基于随机投影技术，并配备了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仿真实验，以展示所提出算法的效率和性能。