A continuous approach to computing the pseudospectra of linear operators
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918130329059328 |
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| author | Deng, Kuan Liu, Xiaolin Xu, Kuan |
| author_facet | Deng, Kuan Liu, Xiaolin Xu, Kuan |
| contents | We propose a continuous approach to computing the pseudospectra of linear operators with compact or compact-plus-scalar resolvent, following a 'solve-then-discretize' strategy. Instead of taking a finite section approach or using a finite-dimensional matrix to approximate the operator of interest, the new method employs an operator analogue of the Lanczos process to work with operators and functions directly. The method is shown to be free of spectral pollution and spectral invisibility, fully adaptive, and nearly optimal in accuracy. The advantages of the method are demonstrated by extensive numerical examples and comparison with the traditional method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03285 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A continuous approach to computing the pseudospectra of linear operators Deng, Kuan Liu, Xiaolin Xu, Kuan Numerical Analysis 65F15, 15A18, 47A10, 47E05, 47G10 We propose a continuous approach to computing the pseudospectra of linear operators with compact or compact-plus-scalar resolvent, following a 'solve-then-discretize' strategy. Instead of taking a finite section approach or using a finite-dimensional matrix to approximate the operator of interest, the new method employs an operator analogue of the Lanczos process to work with operators and functions directly. The method is shown to be free of spectral pollution and spectral invisibility, fully adaptive, and nearly optimal in accuracy. The advantages of the method are demonstrated by extensive numerical examples and comparison with the traditional method. |
| title | A continuous approach to computing the pseudospectra of linear operators |
| topic | Numerical Analysis 65F15, 15A18, 47A10, 47E05, 47G10 |
| url | https://arxiv.org/abs/2405.03285 |