Krylov Subspace Recycling For Matrix Functions
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
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| _version_ | 1866913998276919296 |
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| author | Burke, Liam Frommer, Andreas Ramirez-Hidalgo, Gustavo Soodhalter, Kirk M. |
| author_facet | Burke, Liam Frommer, Andreas Ramirez-Hidalgo, Gustavo Soodhalter, Kirk M. |
| contents | We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive matrices are closely related, but make no assumptions on the relationship between the vectors. We present three versions of the method with different practical implementations. We demonstrate the effectiveness of the method using a range of numerical experiments with a selection of functions and matrices. We primarily focus our attention on the sign function arising in the overlap formalism of lattice QCD. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14163 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Krylov Subspace Recycling For Matrix Functions Burke, Liam Frommer, Andreas Ramirez-Hidalgo, Gustavo Soodhalter, Kirk M. Numerical Analysis 65F10, 65F30, 65F50 We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive matrices are closely related, but make no assumptions on the relationship between the vectors. We present three versions of the method with different practical implementations. We demonstrate the effectiveness of the method using a range of numerical experiments with a selection of functions and matrices. We primarily focus our attention on the sign function arising in the overlap formalism of lattice QCD. |
| title | Krylov Subspace Recycling For Matrix Functions |
| topic | Numerical Analysis 65F10, 65F30, 65F50 |
| url | https://arxiv.org/abs/2209.14163 |