Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (2)

Search Parameters:
Keywords = endpoint geodesics

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
23 pages, 524 KB  
Article
Endpoint Geodesic Formulas on Graßmannians Applied to Interpolation Problems
by Knut Hüper and Fátima Silva Leite
Mathematics 2023, 11(16), 3545; https://doi.org/10.3390/math11163545 - 16 Aug 2023
Cited by 2 | Viewed by 2063
Abstract
Simple closed formulas for endpoint geodesics on Graßmann manifolds are presented. In addition to realizing the shortest distance between two points, geodesics are also essential tools to generate more sophisticated curves that solve higher order interpolation problems on manifolds. This will be illustrated [...] Read more.
Simple closed formulas for endpoint geodesics on Graßmann manifolds are presented. In addition to realizing the shortest distance between two points, geodesics are also essential tools to generate more sophisticated curves that solve higher order interpolation problems on manifolds. This will be illustrated with the geometric de Casteljau construction offering an excellent alternative to the variational approach which gives rise to Riemannian polynomials and splines. Full article
(This article belongs to the Special Issue Variational Methods on Riemannian Manifolds: Theory and Applications)
Show Figures

Figure 1

21 pages, 628 KB  
Article
Transversality Conditions for Geodesics on the Statistical Manifold of Multivariate Gaussian Distributions
by Trevor Herntier and Adrian M. Peter
Entropy 2022, 24(11), 1698; https://doi.org/10.3390/e24111698 - 21 Nov 2022
Cited by 2 | Viewed by 2875
Abstract
We consider the problem of finding the closest multivariate Gaussian distribution on a constraint surface of all Gaussian distributions to a given distribution. Previous research regarding geodesics on the multivariate Gaussian manifold has focused on finding closed-form, shortest-path distances between two fixed distributions [...] Read more.
We consider the problem of finding the closest multivariate Gaussian distribution on a constraint surface of all Gaussian distributions to a given distribution. Previous research regarding geodesics on the multivariate Gaussian manifold has focused on finding closed-form, shortest-path distances between two fixed distributions on the manifold, often restricting the parameters to obtain the desired solution. We demonstrate how to employ the techniques of the calculus of variations with a variable endpoint to search for the closest distribution from a family of distributions generated via a constraint set on the parameter manifold. Furthermore, we examine the intermediate distributions along the learned geodesics which provide insight into uncertainty evolution along the paths. Empirical results elucidate our formulations, with visual illustrations concretely exhibiting dynamics of 1D and 2D Gaussian distributions. Full article
(This article belongs to the Special Issue Information and Divergence Measures)
Show Figures

Figure 1

Back to TopTop