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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2602.19923 |
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| _version_ | 1866908848744300544 |
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| author | Jensen, Rasmus Zimmermann, Ralf |
| author_facet | Jensen, Rasmus Zimmermann, Ralf |
| contents | Retractions are the workhorse in Riemannian computing applications, where computational efficiency is of the essence. This work introduces a new retraction on the compact Stiefel manifold of orthogonal frames. The retraction is second-order accurate under the Euclidean metric and features a closed-form inverse that can be efficiently computed. To the best of our knowledge, this is the first Stiefel retraction with both these properties. A variety of retractions is known on the Stiefel manifold, including the Riemannian exponential map, the polar factor retraction, the QR-retraction and the Cayley retraction, but none of them features a closed-form inverse. The only Stiefel retraction with closed-form inverse that we are aware of is based on quasi-geodesics, but this one is of first order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An new polar factor retraction on the Stiefel manifold with closed-form inverse Jensen, Rasmus Zimmermann, Ralf Numerical Analysis Differential Geometry 15A16, 15B10, 53Z50, 65D05, 65F60 Retractions are the workhorse in Riemannian computing applications, where computational efficiency is of the essence. This work introduces a new retraction on the compact Stiefel manifold of orthogonal frames. The retraction is second-order accurate under the Euclidean metric and features a closed-form inverse that can be efficiently computed. To the best of our knowledge, this is the first Stiefel retraction with both these properties. A variety of retractions is known on the Stiefel manifold, including the Riemannian exponential map, the polar factor retraction, the QR-retraction and the Cayley retraction, but none of them features a closed-form inverse. The only Stiefel retraction with closed-form inverse that we are aware of is based on quasi-geodesics, but this one is of first order. |
| title | An new polar factor retraction on the Stiefel manifold with closed-form inverse |
| topic | Numerical Analysis Differential Geometry 15A16, 15B10, 53Z50, 65D05, 65F60 |
| url | https://arxiv.org/abs/2602.19923 |