extending quasi-gmres method to solve generalized sylvester tensor equations via the einstein product

This paper aims to extend a krylov subspace technique based on an in-complete orthogonalization of krylov tensors (as a multidimensional exten-sion of the common krylov vectors) to solve generalized sylvester tensor equations via the einstein product. first, we obtain the tensor form of the quasi-gmres method, and then we lead to the direct variant of the proposed algorithm. this approach has the great advantage that it uses previous data in each iteration and has a low computational cost. more-over, an upper bound for the residual norm of the approximate solution is found. finally, several experimental problems are given to show the acceptable accuracy and efficiency of the presented method.