M.M. Izadkhah - Department of Computer Science, Faculty of Computer and Industrial Engineering, Birjand University of Technology, Birjand, Iran.

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.

Generalized Sylvester tensor equations, Einstein product, Quasi-GMRES method, Convergence Analysis