A multipoint perturbation formula for eigenvalue problems
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915411436503040 |
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| author | Dusson, Geneviève Garrigue, Louis Stamm, Benjamin |
| author_facet | Dusson, Geneviève Garrigue, Louis Stamm, Benjamin |
| contents | Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several nearby operators are known, standard perturbation theory cannot simultaneously use all this knowledge to provide a better approximation. We derive a resolvent formula enabling such an approximation result, and provide numerical examples for which this method is more competitive than standard perturbation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08151 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A multipoint perturbation formula for eigenvalue problems Dusson, Geneviève Garrigue, Louis Stamm, Benjamin Mathematical Physics Numerical Analysis Spectral Theory Quantum Physics Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several nearby operators are known, standard perturbation theory cannot simultaneously use all this knowledge to provide a better approximation. We derive a resolvent formula enabling such an approximation result, and provide numerical examples for which this method is more competitive than standard perturbation theory. |
| title | A multipoint perturbation formula for eigenvalue problems |
| topic | Mathematical Physics Numerical Analysis Spectral Theory Quantum Physics |
| url | https://arxiv.org/abs/2305.08151 |