Convergence analysis of two-grid methods for symmetric positive semidefinite systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917181313253376 |
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| author | Xu, Xuefeng |
| author_facet | Xu, Xuefeng |
| contents | Two-grid theory plays a fundamental role in the design and analysis of multigrid methods. This paper is devoted to a new convergence analysis of two-grid methods for singular and symmetric positive semidefinite systems. Specifically, we derive a concise identity for characterizing the convergence factor of two-grid methods, with the Moore--Penrose inverse of coarse-grid matrix being used as a coarse solver. Furthermore, we present a convergence estimate for two-grid methods with approximate coarse solvers. Our new theory does not require any additional assumptions on the coefficient matrix, especially on its null space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09442 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of two-grid methods for symmetric positive semidefinite systems Xu, Xuefeng Numerical Analysis Two-grid theory plays a fundamental role in the design and analysis of multigrid methods. This paper is devoted to a new convergence analysis of two-grid methods for singular and symmetric positive semidefinite systems. Specifically, we derive a concise identity for characterizing the convergence factor of two-grid methods, with the Moore--Penrose inverse of coarse-grid matrix being used as a coarse solver. Furthermore, we present a convergence estimate for two-grid methods with approximate coarse solvers. Our new theory does not require any additional assumptions on the coefficient matrix, especially on its null space. |
| title | Convergence analysis of two-grid methods for symmetric positive semidefinite systems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2409.09442 |