On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916156076457984 |
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| author | Wu, Nian-Ci Zuo, Qian Wang, Yatian |
| author_facet | Wu, Nian-Ci Zuo, Qian Wang, Yatian |
| contents | For solving a consistent system of linear equations, the classical row-action (also known as Kaczmarz) method is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy-ball momentum acceleration technique, we propose two deterministic row-action methods and establish the corresponding convergence theory. We show that our algorithm can linearly converge to a least-squares solution with minimum Euclidean norm. Several numerical studies have been presented to corroborate our theoretical findings. Real-world applications, such as data fitting in computer-aided geometry design, are also presented for illustrative purposes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06358 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods Wu, Nian-Ci Zuo, Qian Wang, Yatian Numerical Analysis For solving a consistent system of linear equations, the classical row-action (also known as Kaczmarz) method is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy-ball momentum acceleration technique, we propose two deterministic row-action methods and establish the corresponding convergence theory. We show that our algorithm can linearly converge to a least-squares solution with minimum Euclidean norm. Several numerical studies have been presented to corroborate our theoretical findings. Real-world applications, such as data fitting in computer-aided geometry design, are also presented for illustrative purposes. |
| title | On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2212.06358 |