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math.NA2026
A polar-factor retraction on the symplectic Stiefel manifold with closed-form inverse
Ralf Zimmermann
In Riemannian computing applications, it is crucial to map manifold data to a Euclidean domain, where vector space arithmetic is available, and back. Classical manifold theory guar…
math.NA2024
On the Injectivity Radius of the Stiefel Manifold: Numerical investigations and an explicit construction of a cut point at short distance
Jakob Stoye, Ralf Zimmermann
Arguably, geodesics are the most important geometric objects on a differentiable manifold. They describe candidates for shortest paths and are guaranteed to be unique shortest path…
math.NA2024
High curvature means low-rank: On the sectional curvature of Grassmann and Stiefel manifolds and the underlying matrix trace inequalities
Ralf Zimmermann, Jakob Stoye
Methods and algorithms that work with data on nonlinear manifolds are collectively summarized under the term `Riemannian computing'. In practice, curvature can be a key limiting fa…