Slice tensor splitting method for solving tensor equation

Firstly, we define an (r,r,⋯,r)-slice tensor, and then solve an (r,r,⋯,r)-slice tensor equation by direct method. Secondly, we propose a new splitting of the coefficient tensor to develop a slice tensor splitting method, which is different from the tensor splitting methods in [1,2]. At each iteration of this method, an (r,r,⋯,r)-slice tensor equation is solved. Finally, we prove the local convergence of the proposed method under appropriate conditions, and give numerical experiments to illustrate the effectiveness of this method.