Flexible Modified LSMR Method for Least Squares Problems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912006603276288 |
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| author | Yang, Mei Karaduman, Gul Li, Ren-Cang |
| author_facet | Yang, Mei Karaduman, Gul Li, Ren-Cang |
| contents | LSMR is a widely recognized method for solving least squares problems via the double QR decomposition. Various preconditioning techniques have been explored to improve its efficiency. One issue that arises when implementing these preconditioning techniques is the need to solve two linear systems per iterative step. In this paper, to tackle this issue, among others, a modified LSMR method (MLSMR), in which only one linear system per iterative step needs to be solved instead of two, is introduced, and then it is integrated with the idea of flexible GMRES to yield a flexible MLSMR method (FMLSMR). Numerical examples are presented to demonstrate the efficiency of the proposed FMLSMR method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Flexible Modified LSMR Method for Least Squares Problems Yang, Mei Karaduman, Gul Li, Ren-Cang Numerical Analysis LSMR is a widely recognized method for solving least squares problems via the double QR decomposition. Various preconditioning techniques have been explored to improve its efficiency. One issue that arises when implementing these preconditioning techniques is the need to solve two linear systems per iterative step. In this paper, to tackle this issue, among others, a modified LSMR method (MLSMR), in which only one linear system per iterative step needs to be solved instead of two, is introduced, and then it is integrated with the idea of flexible GMRES to yield a flexible MLSMR method (FMLSMR). Numerical examples are presented to demonstrate the efficiency of the proposed FMLSMR method. |
| title | Flexible Modified LSMR Method for Least Squares Problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2408.16652 |