The paper develops a fast randomized algorithm for computing a hybrid CUR-type decomposition of tensors in the Tucker representation. Specifically, to obtain the factor matrices, random sampling techniques are utilized to accelerate the procedure of constructing the classical matrix decompositions, that are, the interpolatory decomposition and singular value decomposition. Compared with the non-random algorithm, the proposed algorithm has advantages in speed with lower computational cost while keeping a high degree of accuracy. We establish a detailed probabilistic error analysis for the algorithm and provide numerical results that show the promise of our approach.

翻译：本文提出了一种快速随机算法，用于计算张量在Tucker表示下的混合CUR型分解。具体而言，为获得因子矩阵，采用随机采样技术加速经典矩阵分解（即插值分解和奇异值分解）的构建过程。与非随机算法相比，所提算法在保持高精度的同时，具有计算成本更低的速度优势。我们为该算法建立了详细的概率误差分析，并提供了数值结果以验证该方法的有效性。