On convergence of greedy block nonlinear Kaczmarz methods with momentum
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916651704778752 |
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| author | Jiang, Naiyu Bao, Wendi Xing, Lili Li, Weiguo |
| author_facet | Jiang, Naiyu Bao, Wendi Xing, Lili Li, Weiguo |
| contents | In this paper, for solving nonlinear systems we propose two pseudoinverse-free greedy block methods with momentum by combining the residual-based weighted nonlinear Kaczmarz and heavy ball methods. Without the full column rank assumptions on Jacobi matrices of nonlinear systems, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. Numerical experiments demonstrate that the proposed methods with momentum are much more effective than the existing ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10172 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On convergence of greedy block nonlinear Kaczmarz methods with momentum Jiang, Naiyu Bao, Wendi Xing, Lili Li, Weiguo Numerical Analysis In this paper, for solving nonlinear systems we propose two pseudoinverse-free greedy block methods with momentum by combining the residual-based weighted nonlinear Kaczmarz and heavy ball methods. Without the full column rank assumptions on Jacobi matrices of nonlinear systems, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. Numerical experiments demonstrate that the proposed methods with momentum are much more effective than the existing ones. |
| title | On convergence of greedy block nonlinear Kaczmarz methods with momentum |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2503.10172 |