Preconditioned normal equations for solving discretised partial differential equations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912251517075456 |
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| author | Lazzarino, Lorenzo Nakatsukasa, Yuji Zerbinati, Umberto |
| author_facet | Lazzarino, Lorenzo Nakatsukasa, Yuji Zerbinati, Umberto |
| contents | This paper explores preconditioning the normal equation for non-symmetric square linear systems arising from PDE discretization, focusing on methods like CGNE and LSQR. The concept of ``normal'' preconditioning is introduced and a strategy to construct preconditioners studying the associated ``normal'' PDE is presented. Numerical experiments on convection-diffusion problems demonstrate the effectiveness of this approach in achieving fast and stable convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17626 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Preconditioned normal equations for solving discretised partial differential equations Lazzarino, Lorenzo Nakatsukasa, Yuji Zerbinati, Umberto Numerical Analysis 65F08, 65N22, 65H10, 65N30, 65N06, 65N55 This paper explores preconditioning the normal equation for non-symmetric square linear systems arising from PDE discretization, focusing on methods like CGNE and LSQR. The concept of ``normal'' preconditioning is introduced and a strategy to construct preconditioners studying the associated ``normal'' PDE is presented. Numerical experiments on convection-diffusion problems demonstrate the effectiveness of this approach in achieving fast and stable convergence. |
| title | Preconditioned normal equations for solving discretised partial differential equations |
| topic | Numerical Analysis 65F08, 65N22, 65H10, 65N30, 65N06, 65N55 |
| url | https://arxiv.org/abs/2502.17626 |