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

Articles in Press

Document Type : Research Article

Author

• Mohammad Mahdi 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 incomplete orthogonalization of Krylov tensors (as a multidimensional extension 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 low computational cost‎. ‎Moreover‎, ‎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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