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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.19923 |
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Table of 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.