Solving nonlinear eigenvalue problems via contour integration and region partitioning
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910877091889152 |
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| author | Liu, Yuqi Roman, Jose E. Shao, Meiyue |
| author_facet | Liu, Yuqi Roman, Jose E. Shao, Meiyue |
| contents | In this work, we combine Beyn's method and the recently developed recursive integral method (RIM) to propose a contour integral-based, region partitioning eigensolver for nonlinear eigenvalue problems. A new partitioning criterion is employed to eliminate the need for a problem-dependent parameter, making our algorithm much more robust compared to the original RIM. Moreover, our algorithm can be directly applied to regions containing singularities or accumulation points, which are typically challenging for existing nonlinear eigensolvers to handle. Comprehensive numerical experiments are provided to demonstrate that the proposed algorithm is particularly well suited for dealing with regions including many eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving nonlinear eigenvalue problems via contour integration and region partitioning Liu, Yuqi Roman, Jose E. Shao, Meiyue Numerical Analysis 65F10, 65F15, 65F50 In this work, we combine Beyn's method and the recently developed recursive integral method (RIM) to propose a contour integral-based, region partitioning eigensolver for nonlinear eigenvalue problems. A new partitioning criterion is employed to eliminate the need for a problem-dependent parameter, making our algorithm much more robust compared to the original RIM. Moreover, our algorithm can be directly applied to regions containing singularities or accumulation points, which are typically challenging for existing nonlinear eigensolvers to handle. Comprehensive numerical experiments are provided to demonstrate that the proposed algorithm is particularly well suited for dealing with regions including many eigenvalues. |
| title | Solving nonlinear eigenvalue problems via contour integration and region partitioning |
| topic | Numerical Analysis 65F10, 65F15, 65F50 |
| url | https://arxiv.org/abs/2503.12038 |