Extending quasi-GMRES method to solve generalized Sylvester tensor equations via the Einstein product

Document Type : Research Article

Author

• M.M. Izadkhah

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

10.22067/ijnao.2024.87481.1418

Abstract

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.

Keywords

• Generalized Sylvester tensor equations
• Einstein product
• Quasi-GMRES method
• Convergence analysis

Main Subjects

• Numerical linear algebra and its applications

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