A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations

This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive preconditioned based on Kronecker product approximations A theoretical analysis shows that proposed converges an exact solution any initial at most finite steps in absence round-off errors. Compared with gradient method, obtained numerical results illustrate our methods perform much better terms of number iteration and computing time.