An inexact Matrix-Newton method for solving NEPv
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916378223575040 |
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| author | Werner, Tom |
| author_facet | Werner, Tom |
| contents | In this paper, an inexact Newton method for solving real-valued nonlinear eigenvalue problems with eigenvector dependency (NEPv) is introduced that is able to solve the problem on a matrix level. Our main contribution is to derive a variant of Newton's method that uses global Krylov methods such as global GMRES to solve the linear operator equation necessary to compute the Newton correction in a matrix-free way. The advantages that this second order method has over the well-established SCF algorithm are explained and visualized by a variety of numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_09670 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An inexact Matrix-Newton method for solving NEPv Werner, Tom Numerical Analysis In this paper, an inexact Newton method for solving real-valued nonlinear eigenvalue problems with eigenvector dependency (NEPv) is introduced that is able to solve the problem on a matrix level. Our main contribution is to derive a variant of Newton's method that uses global Krylov methods such as global GMRES to solve the linear operator equation necessary to compute the Newton correction in a matrix-free way. The advantages that this second order method has over the well-established SCF algorithm are explained and visualized by a variety of numerical experiments. |
| title | An inexact Matrix-Newton method for solving NEPv |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2311.09670 |