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- Title
Deflated and restarted Krylov subspace methods for Sylvester tensor equations.
- Authors
Gu, Ying; Wu, Gang; Zhang, Xin
- Abstract
Tensor Krylov subspace methods are popular technologies for solving Sylvester tensor equations, among which the GMRES method based on tensor format (GMRES_BTF) and the FOM method based on tensor format (FOM_BTF) are two commonly used ones. Both of them rely on the Arnoldi process based on tensor format (Arnoldi_BTF) to construct orthonormal bases for tensor Krylov subspace. However, the computational costs and storage requirements of the tensor Krylov subspace methods will increase tremendously as the Arnoldi_BTF process proceeds. Restarting is an efficient way to deal with this problem. To the best of our knowledge, there are few efficient restarting strategies for tensor Krylov subspace methods. In order to fill-in this gap, we apply the deflated restarting strategy to the GMRES_BTF and FOM_BTF methods, and propose two deflated restating methods for solving Sylvester tensor equations. The key is that the two proposed methods retain some useful information in the harmonic Ritz tensors or Ritz tensors obtained from the previous tensor Krylov subspace, respectively. Numerical experiments on both artificial and real data sets demonstrate the superiority of the proposed methods over many state-of-the-art methods for Sylvester tensor equations.
- Subjects
KRYLOV subspace; SYLVESTER matrix equations
- Publication
Calcolo, 2023, Vol 60, Issue 3, p1
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-023-00532-6