Reduced order method based Anderson-type acceleration method for nonlinear least square problems and large scale ill-posed problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909930193158144 |
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| author | Ito, Kazufumi Xue, Tiancheng |
| author_facet | Ito, Kazufumi Xue, Tiancheng |
| contents | In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next iterate by minimizing the equation error over the linear manifold spanned by this basis. The resulting optimal linear combination yields a more accurate approximation of the solution and significantly enhances convergence. In essence, the method can be seen as a history-based acceleration technique, akin to a delayed or memory-enhanced iterative scheme. This approach effectively remedies semi-ill-posed problems, enabling convergence where standard methods may fail, and also acts as a stabilizing and regularizing mechanism for the original iteration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reduced order method based Anderson-type acceleration method for nonlinear least square problems and large scale ill-posed problems Ito, Kazufumi Xue, Tiancheng Numerical Analysis Optimization and Control In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next iterate by minimizing the equation error over the linear manifold spanned by this basis. The resulting optimal linear combination yields a more accurate approximation of the solution and significantly enhances convergence. In essence, the method can be seen as a history-based acceleration technique, akin to a delayed or memory-enhanced iterative scheme. This approach effectively remedies semi-ill-posed problems, enabling convergence where standard methods may fail, and also acts as a stabilizing and regularizing mechanism for the original iteration. |
| title | Reduced order method based Anderson-type acceleration method for nonlinear least square problems and large scale ill-posed problems |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2510.15097 |