On sketch-and-project methods for solving tensor equations

Abstract

We propose a regular sketch-and-project method for solving linear tensor equations based on the t-product and present its equivalent Fourier domain version, along with several special cases corresponding to existing classical matrix equation methods. Furthermore, we extend this framework via a hierarchical approach to solve generalized Sylvester tensor equations. All the methods are proved to converge linearly in expectation. Finally, numerical experiments demonstrate the efficiency and effectiveness of the proposed approach.