A projection method and Kronecker product preconditioner for solving Sylvester tensor equations

The preconditioned iterative solvers for solving Sylvester tensor equations are considered in this paper. By fully exploiting the structure of the tensor equation, we propose a projection method based on the tensor format, which needs less flops and storage than the standard projection method. The structure of the coefficient matrices of the tensor equation is used to design the nearest Kronecker product (NKP) preconditioner, which is easy to construct and is able to accelerate the convergence of the iterative solver. Numerical experiments are presented to show good performance of the approaches.