Conditioning and backward errors for nonlinear eigenvalue problems with eigenvector nonlinearities
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910239988645888 |
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| author | Lithell, Vilhelm Peterson Janssens, Victor Jarlebring, Elias Meerbergen, Karl Michiels, Wim |
| author_facet | Lithell, Vilhelm Peterson Janssens, Victor Jarlebring, Elias Meerbergen, Karl Michiels, Wim |
| contents | We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be evaluated with little computational effort for a given eigenpair, assuming the matrix perturbations are measured by the spectral or Frobenius norm. We also show how symmetric perturbations can be exploited in the analysis. By means of two numerical experiments we demonstrate that problems incorporating eigenvector nonlinearities potentially need to be treated with additional care, when compared to the linear or eigenvalue-nonlinear theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20933 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conditioning and backward errors for nonlinear eigenvalue problems with eigenvector nonlinearities Lithell, Vilhelm Peterson Janssens, Victor Jarlebring, Elias Meerbergen, Karl Michiels, Wim Numerical Analysis 35P30, 65H17, 15A18, 65F15 We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be evaluated with little computational effort for a given eigenpair, assuming the matrix perturbations are measured by the spectral or Frobenius norm. We also show how symmetric perturbations can be exploited in the analysis. By means of two numerical experiments we demonstrate that problems incorporating eigenvector nonlinearities potentially need to be treated with additional care, when compared to the linear or eigenvalue-nonlinear theory. |
| title | Conditioning and backward errors for nonlinear eigenvalue problems with eigenvector nonlinearities |
| topic | Numerical Analysis 35P30, 65H17, 15A18, 65F15 |
| url | https://arxiv.org/abs/2605.20933 |