Matrix-free stochastic calculation of operator norms without using adjoints
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917120376307712 |
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| author | Bresch, Jonas Lorenz, Dirk A. Schneppe, Felix Winkler, Maximilian |
| author_facet | Bresch, Jonas Lorenz, Dirk A. Schneppe, Felix Winkler, Maximilian |
| contents | This paper considers the problem of computing the operator norm of a linear map between finite dimensional Hilbert spaces when only evaluations of the linear map are available and under restrictive storage assumptions. We propose a stochastic method of random search type to maximize the Rayleigh quotient and employ an exact line search in the random search directions. Moreover, we show that the proposed algorithm converges to the global maximum (the operator norm) almost surely and a sublinear convergence behavior for the corresponding eigenvector and eigenvalue equation. Finally, we illustrate the performance of the method with numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matrix-free stochastic calculation of operator norms without using adjoints Bresch, Jonas Lorenz, Dirk A. Schneppe, Felix Winkler, Maximilian Numerical Analysis 65F35, 15A60, 68W20 This paper considers the problem of computing the operator norm of a linear map between finite dimensional Hilbert spaces when only evaluations of the linear map are available and under restrictive storage assumptions. We propose a stochastic method of random search type to maximize the Rayleigh quotient and employ an exact line search in the random search directions. Moreover, we show that the proposed algorithm converges to the global maximum (the operator norm) almost surely and a sublinear convergence behavior for the corresponding eigenvector and eigenvalue equation. Finally, we illustrate the performance of the method with numerical experiments. |
| title | Matrix-free stochastic calculation of operator norms without using adjoints |
| topic | Numerical Analysis 65F35, 15A60, 68W20 |
| url | https://arxiv.org/abs/2410.08297 |