Inner Product Free Krylov Methods for Large-Scale Inverse Problems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910595064791040 |
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| author | Brown, Ariana N. Chung, Julianne Nagy, James G. Landman, Malena Sabaté |
| author_facet | Brown, Ariana N. Chung, Julianne Nagy, James G. Landman, Malena Sabaté |
| contents | In this study, we introduce two new Krylov subspace methods for solving rectangular large-scale linear inverse problems. The first approach is a modification of the Hessenberg iterative algorithm that is based off an LU factorization and is therefore referred to as the least squares LU (LSLU) method. The second approach incorporates Tikhonov regularization in an efficient manner; we call this the Hybrid LSLU method. Both methods are inner-product free, making them advantageous for high performance computing and mixed precision arithmetic. Theoretical findings and numerical results show that Hybrid LSLU can be effective in solving large-scale inverse problems and has comparable performance with existing iterative projection methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05239 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inner Product Free Krylov Methods for Large-Scale Inverse Problems Brown, Ariana N. Chung, Julianne Nagy, James G. Landman, Malena Sabaté Numerical Analysis 65F22, 65F10, 65K10, 15A29 In this study, we introduce two new Krylov subspace methods for solving rectangular large-scale linear inverse problems. The first approach is a modification of the Hessenberg iterative algorithm that is based off an LU factorization and is therefore referred to as the least squares LU (LSLU) method. The second approach incorporates Tikhonov regularization in an efficient manner; we call this the Hybrid LSLU method. Both methods are inner-product free, making them advantageous for high performance computing and mixed precision arithmetic. Theoretical findings and numerical results show that Hybrid LSLU can be effective in solving large-scale inverse problems and has comparable performance with existing iterative projection methods. |
| title | Inner Product Free Krylov Methods for Large-Scale Inverse Problems |
| topic | Numerical Analysis 65F22, 65F10, 65K10, 15A29 |
| url | https://arxiv.org/abs/2409.05239 |