The sparse Kaczmarz method with surrogate hyperplane for the regularized basis pursuit problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909228901335040 |
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| author | Wang, Ze Yin, Jun-Feng Zhao, Ji-Chen |
| author_facet | Wang, Ze Yin, Jun-Feng Zhao, Ji-Chen |
| contents | The Sparse Kaczmarz method is a famous and widely used iterative method for solving the regularized basis pursuit problem. A general scheme of the surrogate hyperplane sparse Kaczmarz method is proposed. In particular, a class of residual-based surrogate hyperplane sparse Kaczmarz method is introduced and the implementations are well discussed. Their convergence theories are proved and the linear convergence rates are studied and compared in details. Numerical experiments verify the efficiency of the proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The sparse Kaczmarz method with surrogate hyperplane for the regularized basis pursuit problem Wang, Ze Yin, Jun-Feng Zhao, Ji-Chen Numerical Analysis The Sparse Kaczmarz method is a famous and widely used iterative method for solving the regularized basis pursuit problem. A general scheme of the surrogate hyperplane sparse Kaczmarz method is proposed. In particular, a class of residual-based surrogate hyperplane sparse Kaczmarz method is introduced and the implementations are well discussed. Their convergence theories are proved and the linear convergence rates are studied and compared in details. Numerical experiments verify the efficiency of the proposed methods. |
| title | The sparse Kaczmarz method with surrogate hyperplane for the regularized basis pursuit problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2406.15082 |