A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909458945277952 |
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| author | Eisenmann, Henrik |
| author_facet | Eisenmann, Henrik |
| contents | We present a new approach to compute eigenvalues and eigenvectors of locally definite multiparameter eigenvalue problems by its signed multiindex. The method has the interpretation of a semismooth Newton method applied to certain functions that have a unique zero. We can therefore show local quadratic convergence, and for certain extreme eigenvalues even global linear convergence of the method. Local definiteness is a weaker condition than right and left definiteness, which is often considered for multiparameter eigenvalue problems. These conditions are naturally satisfied for multiparameter Sturm-Liouville problems that arise when separation of variables can be applied to multidimensional boundary eigenvalue problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04194 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex Eisenmann, Henrik Numerical Analysis 65F15, 15A18, 15A69 We present a new approach to compute eigenvalues and eigenvectors of locally definite multiparameter eigenvalue problems by its signed multiindex. The method has the interpretation of a semismooth Newton method applied to certain functions that have a unique zero. We can therefore show local quadratic convergence, and for certain extreme eigenvalues even global linear convergence of the method. Local definiteness is a weaker condition than right and left definiteness, which is often considered for multiparameter eigenvalue problems. These conditions are naturally satisfied for multiparameter Sturm-Liouville problems that arise when separation of variables can be applied to multidimensional boundary eigenvalue problems. |
| title | A Newton method for solving locally definite multiparameter eigenvalue problems by multiindex |
| topic | Numerical Analysis 65F15, 15A18, 15A69 |
| url | https://arxiv.org/abs/2404.04194 |