论文标题
关于求解张量方程的草图和项目的方法
On sketch-and-project methods for solving tensor equations
论文作者
论文摘要
我们首先提出了针对流行的T产品求解张量方程的常规草图和项目。然后，得出了三种自适应抽样策略和三种相应的自适应草图和项目。我们证明所有提出的方法都具有期望的线性收敛。此外，我们研究了新方法的傅立叶域版本和一些特殊情况，其中后者对应于一些著名的矩阵方程方法。最后，提出了数值实验，以证明和测试提出的解决张量方程的方法的可行性和有效性
We first propose the regular sketch-and-project method for solving tensor equations with respect to the popular t-product. Then, three adaptive sampling strategies and three corresponding adaptive sketch-and-project methods are derived. We prove that all the proposed methods have linear convergence in expectation. Furthermore, we investigate the Fourier domain versions and some special cases of the new methods, where the latter corresponds to some famous matrix equation methods. Finally, numerical experiments are presented to demonstrate and test the feasibility and effectiveness of the proposed methods for solving tensor equations
