A gradient flow method for smooth splines versus least-squares fitting on Riemannian manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914815260229632 |
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| author | Lin, Chun-Chi Tran, The Dung |
| author_facet | Lin, Chun-Chi Tran, The Dung |
| contents | This article presents a novel resolution to the problem of spline interpolation versus least-squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of networks. This approach represents a contribution to both geometric control theory and statistical shape data analysis. Our work encompasses a rigorous proof for the existence of global solutions in Hölder spaces for the gradient flow. The asymptotic limits of these solutions establish the existence of the spline interpolation versus least-squares fitting problem on smooth Riemannian manifolds, offering a comprehensive solution. Notably, the constructive nature of the proof suggests potential numerical schemes for finding solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A gradient flow method for smooth splines versus least-squares fitting on Riemannian manifolds Lin, Chun-Chi Tran, The Dung Optimization and Control primary 35K52, 49J20, secondary 41A15, 35K25 This article presents a novel resolution to the problem of spline interpolation versus least-squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of networks. This approach represents a contribution to both geometric control theory and statistical shape data analysis. Our work encompasses a rigorous proof for the existence of global solutions in Hölder spaces for the gradient flow. The asymptotic limits of these solutions establish the existence of the spline interpolation versus least-squares fitting problem on smooth Riemannian manifolds, offering a comprehensive solution. Notably, the constructive nature of the proof suggests potential numerical schemes for finding solutions. |
| title | A gradient flow method for smooth splines versus least-squares fitting on Riemannian manifolds |
| topic | Optimization and Control primary 35K52, 49J20, secondary 41A15, 35K25 |
| url | https://arxiv.org/abs/2402.18067 |