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
翻译:我们首先提出解决流行的T产品高方程的常规草图和项目方法,然后提出三个适应性抽样战略和三个相应的适应性草图和项目方法。我们证明所有拟议方法都有预期的线性趋同。此外,我们调查了Fourier域版和新方法的一些特殊案例,后者与一些著名的矩阵方程方法相对应。最后,进行了数字实验,以示范和测试解决数方程的拟议方法的可行性和有效性。