@inproceedings{4d15579dfb2a432ca98a8a5747f70eda,

title = "Efficient Quasi-Geodesics on the Stiefel Manifold",

abstract = "Solving the so-called geodesic endpoint problem, i.e., finding a geodesic that connects two given points on a manifold, is at the basis of virtually all data processing operations, including averaging, clustering, interpolation and optimization. On the Stiefel manifold of orthonormal frames, this problem is computationally involved. A remedy is to use quasi-geodesics as a replacement for the Riemannian geodesics. Quasi-geodesics feature constant speed and covariant acceleration with constant (but possibly non-zero) norm. For a well-known type of quasi-geodesics, we derive a new representation that is suited for large-scale computations. Moreover, we introduce a new kind of quasi-geodesics that turns out to be much closer to the Riemannian geodesics.",

keywords = "Stiefel Manifold, Geodesic, Quasi-geodesic, Geodesic Endpoint Problem, Stiefel manifold, Geodesic endpoint problem",

author = "Thomas Bendokat and Ralf Zimmermann",

note = "1) Peer review<br/>2) arxiv version of accepted contribution to the proceedings of the <br/>5th conference on Geometric Science of Information in PARIS, Sorbonne University; 5th International Conference, GSI 2021 ; Conference date: 21-07-2021 Through 23-07-2021",

year = "2021",

month = jul,

day = "14",

doi = "10.1007/978-3-030-80209-7_82",

language = "English",

isbn = "978-3-030-80208-0",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "763--771",

editor = "Frank Nielsen and Fr{\'e}d{\'e}ric Barbaresco",

booktitle = "Geometric Science of Information",

address = "Germany",

}