69 citations · 101 across the 10 of their papers we have counts for
10 papers
Multivariate Hermite interpolation of manifold-valued data
Ralf Zimmermann, Ronny Bergmann
In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted…
Sliced gradient-enhanced Kriging for high-dimensional function approximation
Kai Cheng, Ralf Zimmermann
Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modelling technique for approximating expensive computational models. However, it tends to get impractical fo…
The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications
Thomas Bendokat, Ralf Zimmermann
The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and…
Efficient Quasi-Geodesics on the Stiefel Manifold
Thomas Bendokat, Ralf Zimmermann
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,…
Computing the Riemannian logarithm on the Stiefel manifold: metrics, methods and performance
Ralf Zimmermann, Knut Hüper
We address the problem of computing Riemannian normal coordinates on the real, compact Stiefel manifold of orthogonal frames. The Riemannian normal coordinates are based on the so-…
A Grassmann Manifold Handbook: Basic Geometry and Computational Aspects
Thomas Bendokat, Ralf Zimmermann, P. -A. Absil
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision an…
Hermite interpolation and data processing errors on Riemannian matrix manifolds
Ralf Zimmermann
The main contribution of this paper is twofold: On the one hand, a general framework for performing Hermite interpolation on Riemannian manifolds is presented. The method is applic…
Manifold interpolation and model reduction
Ralf Zimmermann
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sample…
A geometric note on subspace updates and orthogonal matrix decompositions under rank-one modifications
Ralf Zimmermann
In this work, we consider rank-one adaptations of a given matrix with known matrix factorization , where $U\in\mathbb{R}^{n…
A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold under the canonical metric
Ralf Zimmermann
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based…