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Journal Articles Journal of Computational and Applied Mathematics Year : 2020

A tensor format for the generalized Hessenberg method for solving Sylvester tensor equations

Abstract

In this paper, a general framework using tensor Krylov projection techniques is proposed for solving high order Sylvester tensor equations. After describing the tensor format of the generalized Hessenberg process, we combine the obtained different processes with a Galerkin orthogonality condition or with a minimal norm condition in order to derive the Hess−BTF and CMRH−BTF methods which are based on the tensor format of the Hessenberg process. In addition, we also recover the FOM−BTF and GMRES−BTF which are known methods based on the tensor format of the Arnoldi process. To accelerate the convergence or prevent a possible stagnation of the different obtained methods, we incorporate a weighting strategy based on the use of a weighted inner product instead of the classical one when building a basis for the tensor Krylov subspace. Numerical experiments are described in order to compare the new proposed methods that are Hess−BTF and CMRH−BTF with the known methods FOM−BTF and GMRES−BTF and to show the efficiency of the weighting strategy. Moreover, we utilize a flexible preconditioning framework for the unweighted and weighted forms of the proposed methods, and the flexible version is validated by satisfactory numerical results.
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Dates and versions

hal-04413590 , version 1 (23-01-2024)

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Mohammed Heyouni, Farid Saberi-Movahed, Azita Tajaddini. A tensor format for the generalized Hessenberg method for solving Sylvester tensor equations. Journal of Computational and Applied Mathematics, 2020, 377, pp.112878. ⟨10.1016/j.cam.2020.112878⟩. ⟨hal-04413590⟩
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