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We first propose the regular sketch-and-project method for solving tensorequations with respect to the popular t-product. Then, three adaptive samplingstrategies and three corresponding adaptive sketch-and-project methods arederived. We prove that all the proposed methods have linear convergence inexpectation. Furthermore, we investigate the Fourier domain versions and somespecial cases of the new methods, where the latter corresponds to some famousmatrix equation methods. Finally, numerical experiments are presented todemonstrate and test the feasibility and effectiveness of the proposed methodsfor solving tensor equations

On sketch-and-project methods for solving tensor equations