A generalized spectral concentration problem and the varying masks algorithm
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912055648321536 |
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| author | Faou, Erwan Henaff, Yoann Le |
| author_facet | Faou, Erwan Henaff, Yoann Le |
| contents | In this paper we generalize the spectral concentration problem as formulated by Slepian, Pollak and Landau in the 1960s. We show that a generalized version with arbitrary space and Fourier masks is well-posed, and we prove some new results concerning general quadratic domains and gaussian filters. We also propose a more general splitting representation of the spectral concentration operator allowing to construct quasi-modes in some situations. We then study its discretization and we illustrate the fact that standard eigen-algorithms are not robust because of a clustering of eigenvalues. We propose a new alternative algorithm that can be implemented in any dimension and for any domain shape, and that gives very efficient results in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalized spectral concentration problem and the varying masks algorithm Faou, Erwan Henaff, Yoann Le Numerical Analysis Spectral Theory In this paper we generalize the spectral concentration problem as formulated by Slepian, Pollak and Landau in the 1960s. We show that a generalized version with arbitrary space and Fourier masks is well-posed, and we prove some new results concerning general quadratic domains and gaussian filters. We also propose a more general splitting representation of the spectral concentration operator allowing to construct quasi-modes in some situations. We then study its discretization and we illustrate the fact that standard eigen-algorithms are not robust because of a clustering of eigenvalues. We propose a new alternative algorithm that can be implemented in any dimension and for any domain shape, and that gives very efficient results in practice. |
| title | A generalized spectral concentration problem and the varying masks algorithm |
| topic | Numerical Analysis Spectral Theory |
| url | https://arxiv.org/abs/2410.01465 |