Tensor wheel (TW) decomposition combines the popular tensor ring and fully connected tensor network decompositions and has achieved excellent performance in tensor completion problem. A standard method to compute this decomposition is the alternating least squares (ALS). However, it usually suffers from slow convergence and numerical instability. In this work, the fast and robust SVD-based algorithms are investigated. Based on a result on TW-ranks, we first propose a deterministic algorithm that can estimate the TW decomposition of the target tensor under a controllable accuracy. Then, the randomized versions of this algorithm are presented, which can be divided into two categories and allow various types of sketching. Numerical results on synthetic and real data show that our algorithms have much better performance than the ALS-based method and are also quite robust. In addition, with one SVD-based algorithm, we also numerically explore the variability of TW decomposition with respect to TW-ranks and the comparisons between TW decomposition and other famous formats in terms of the performance on approximation and compression.

张量轮（TW）分解结合了流行的张量环和全连接张量网络分解，在张量完成问题上取得了优异的性能。计算此分解的标准方法是交替最小二乘法 (ALS)。然而，它通常会遇到收敛速度慢和数值不稳定的问题。在这项工作中，研究了快速且鲁棒的基于 SVD 的算法。基于TW-ranks的结果，我们首先提出了一种确定性算法，可以在可控的精度下估计目标张量的TW分解。然后，提出了该算法的随机版本，它可以分为两类并允许各种类型的草图。合成数据和真实数据的数值结果表明，我们的算法比基于 ALS 的方法具有更好的性能，并且也非常稳健。此外，通过一种基于 SVD 的算法，我们还以数值方式探讨了 TW 分解相对于 TW 秩的可变性，以及 TW 分解与其他著名格式在逼近和压缩性能方面的比较。