Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911885561954304 |
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| author | Bergamaschi, Luca Martinez, Angeles Pearson, John Potschka, Andreas |
| author_facet | Bergamaschi, Luca Martinez, Angeles Pearson, John Potschka, Andreas |
| contents | In this paper, we describe and analyze the spectral properties of a symmetric positive definite inexact block preconditioner for a class of symmetric, double saddle-point linear systems.
We develop a spectral analysis of the preconditioned matrix, showing that its eigenvalues can be described in terms of the roots of a cubic polynomial with real coefficients.
We illustrate the efficiency of the proposed preconditioners, and verify the theoretical bounds, in solving large-scale PDE-constrained optimization problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14605 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization Bergamaschi, Luca Martinez, Angeles Pearson, John Potschka, Andreas Numerical Analysis In this paper, we describe and analyze the spectral properties of a symmetric positive definite inexact block preconditioner for a class of symmetric, double saddle-point linear systems. We develop a spectral analysis of the preconditioned matrix, showing that its eigenvalues can be described in terms of the roots of a cubic polynomial with real coefficients. We illustrate the efficiency of the proposed preconditioners, and verify the theoretical bounds, in solving large-scale PDE-constrained optimization problems. |
| title | Spectral analysis of block preconditioners for double saddle-point linear systems with application to PDE-constrained optimization |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.14605 |