Convergence of the vertical Gradient flow for the Gaussian Monge problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917848032477184 |
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| author | Jansson, Erik Modin, Klas |
| author_facet | Jansson, Erik Modin, Klas |
| contents | We investigate a matrix dynamical system related to optimal mass transport in the linear category, namely, the problem of finding an optimal invertible matrix by which two covariance matrices are congruent. We first review the differential geometric structure of the problem in terms of a principal fiber bundle. The dynamical system is a gradient flow restricted to the fibers of the bundle. We prove global existence of solutions to the flow, with convergence to the polar decomposition of the matrix given as initial data. The convergence is illustrated in a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19788 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence of the vertical Gradient flow for the Gaussian Monge problem Jansson, Erik Modin, Klas Optimization and Control Differential Geometry 15A23, 49M99, 49Q22 We investigate a matrix dynamical system related to optimal mass transport in the linear category, namely, the problem of finding an optimal invertible matrix by which two covariance matrices are congruent. We first review the differential geometric structure of the problem in terms of a principal fiber bundle. The dynamical system is a gradient flow restricted to the fibers of the bundle. We prove global existence of solutions to the flow, with convergence to the polar decomposition of the matrix given as initial data. The convergence is illustrated in a numerical example. |
| title | Convergence of the vertical Gradient flow for the Gaussian Monge problem |
| topic | Optimization and Control Differential Geometry 15A23, 49M99, 49Q22 |
| url | https://arxiv.org/abs/2305.19788 |