论文标题
张量线性系统的草图和项目
Sketch-and-project methods for tensor linear systems
论文作者
论文摘要
对于张量相对于流行的T产品，我们首先介绍草图和项目的自适应变体。还研究了他们的傅立叶域版本。然后，考虑到现有的草图张量或抽样方式有一些局限性，我们提出了两种改进的策略。提供了上述方法的收敛分析。我们使用合成和真实数据将我们的方法与现有方法进行比较。数值结果表明，在迭代次数和运行时间方面，它们具有相当不错的性能。
For tensor linear systems with respect to the popular t-product, we first present the sketch-and-project method and its adaptive variants. Their Fourier domain versions are also investigated. Then, considering that the existing sketching tensor or way for sampling has some limitations, we propose two improved strategies. Convergence analyses for the methods mentioned above are provided. We compare our methods with the existing ones using synthetic and real data. Numerical results show that they have quite decent performance in terms of the number of iterations and running time.
