Zobrazeno 1 - 10
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pro vyhledávání: '"Zimmermann, Ralf"'
Autor:
Zimmermann, Ralf, Stoye, Jakob
The injectivity radius of a manifold is an important quantity, both from a theoretical point of view and in terms of numerical applications. It is the largest possible radius within which all geodesics are unique and length-minimizing. In consequence
Externí odkaz:
http://arxiv.org/abs/2405.02268
Autor:
Jensen, Rasmus, Zimmermann, Ralf
Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall into this category, where the manifold is usually specified by special
Externí odkaz:
http://arxiv.org/abs/2404.08463
Since the popularization of the Stiefel manifold for numerical applications in 1998 in a seminal paper from Edelman et al., it has been exhibited to be a key to solve many problems from optimization, statistics and machine learning. In 2021, H\"uper
Externí odkaz:
http://arxiv.org/abs/2403.11730
Autor:
Stoye, Jakob, Zimmermann, Ralf
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 paths when the starting velocity stays within the so-called injectivity ra
Externí odkaz:
http://arxiv.org/abs/2403.03782
Autor:
Zimmermann, Ralf, Stoye, Jakob
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 factor for the performance of Riemannian computing methods. Yet, curvatu
Externí odkaz:
http://arxiv.org/abs/2403.01879
Autor:
Zimmermann, Ralf, Bergmann, Ronny
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 Riemannian barycenters. To satisfy the conditions for Hermite interpol
Externí odkaz:
http://arxiv.org/abs/2212.07281
Autor:
Zimmermann, Ralf, Romeis, Dirk, Bihannic, Isabelle, Stuart, Martien Cohen, Sommer, Jens-Uwe, Werner, Carsten
Unravelling details of charge, structure and molecular interactions of functional polymer coatings defines an important analytical challenge that requires the extension of current methodologies. In this article we demonstrate how streaming current me
Externí odkaz:
https://tud.qucosa.de/id/qucosa%3A36401
https://tud.qucosa.de/api/qucosa%3A36401/attachment/ATT-0/
https://tud.qucosa.de/api/qucosa%3A36401/attachment/ATT-0/
Autor:
Cheng, Kai, Zimmermann, Ralf
Publikováno v:
SIAM Journal on Scientific Computing, 2023
Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modelling technique for approximating expensive computational models. However, it tends to get impractical for high-dimensional problems due to the size of the inherent correlatio
Externí odkaz:
http://arxiv.org/abs/2204.03562
Autor:
Hartikainen, Anni H., Basnet, Satish, Yli-Pirilä, Pasi, Ihalainen, Mika, Talvinen, Sini, Tissari, Jarkko, Mikkonen, Santtu, Zimmermann, Ralf, Sippula, Olli
Publikováno v:
In Combustion and Flame July 2024 265