Transpose-free quasi-minimal residual method based on tensor format for generalized coupled Sylvester tensor equations

This paper presents an extension of the transpose-free quasi-minimal residual (TFQMR) method for solving the generalized coupled Sylvester tensor equations. The new algorithm is based on the tensor format of the TFQMR process. We analyze the convergence behavior of this method and present a bound for the residual norm of the method depending on the specific parameter computed by the algorithm. The numerical experiments demonstrate the efficiency of the new method and confirm the theoretical results.