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

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Izadkhah M.M.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2024 | Volume:14 | Issue:3 Page(s): 938-969

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Information Journal Paper

Title

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

Author(s)

Izadkhah M.M. | Issue Writer Certificate

Keywords

Generalized Sylvester tensor equations

Einstein product

Quasi-GMRES method

Convergence Analysis

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.

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