• Keine Ergebnisse gefunden

Im Rahmen des Promotionsprogramm „Data Science: Mathematical Analysis, Scalable Algorithms, and Systems”

N/A
N/A
Protected

Academic year: 2021

Aktie "Im Rahmen des Promotionsprogramm „Data Science: Mathematical Analysis, Scalable Algorithms, and Systems”"

Copied!
1
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Volltext

(1)

Im Rahmen des Promotionsprogramm

„Data Science: Mathematical Analysis, Scalable Algorithms, and Systems”

wird

Frau Prof. Dr. Gabriele Steidl, TU Kaiserlautern,

am Mittwoch, 19. Februar 2020,

zum Thema

„Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization”

vortragen.

Abstract.

The approximation of probability measures on compact metric spaces and in particular on Riemannian manifolds by atomic or empirical ones is a classical task in approximation and complexity theory with a wide range of applications. Instead of point measures we are concerned with the approximation by measures supported on Lipschitz curves. Special attention is paid to push-forward measures of Lebesgue measures on the interval by such curves. Using the discrepancy as distance between measures, we prove optimal approximation rates in terms of Lipschitz constants of curves. Having established the theoretical convergence rates, we are interested in the numerical minimization of the discrepancy between a given probability measure and the set of push- forward measures of Lebesgue measures on the interval by Lipschitz curves. We present numerical examples for measures on the 2- and 3-dimensional torus, the 2-sphere, the rotation group in 3D and the Grassmannian of all 2-dimensional linear subspaces of the four-dimensional Euclidean space.

Our algorithm of choice is a conjugate gradient method on these manifolds which incorporates second-order information. For efficiently computing the gradients and the Hessians within the algorithm, we approximate the given measures by truncated Fourier series and use fast Fourier transform techniques on these manifolds Joint work with M. Ehler, M. Gräf and S. Neumayer.

Der Vortrag findet um 16:30 Uhr im HS IV, 04A30, am Fachbereich Mathematik und Informatik, Lahnberge, statt.

Kaffee/Tee im SR VII, 05D01, um 16:00 Uhr.

Es laden ein die Dozenten des

Promotionsprogramms

Referenzen

ÄHNLICHE DOKUMENTE

Here we can recognize one of the motives for Leonardos insistence on proportion and the measure of sight: the correct measure of sight and thus the rationality of perspective

The definition of free will from section 2.1 is obviously different from the core idea (moral responsibility is a necessary condition of freedom of will) of compatibilism

From top to bottom: raw mechanical signal in the time domain; one-sided Fourier spectrum; two short-time Fourier spectra (STFT) spectrograms with small rectangular windows of 2 7

In 1970, for example, the group of females aged 20-24 years (Table 1) comprised 11.24 percent of the population having completed a degree of education higher than primary, as opposed

In general, the competitiveness of the European forest cluster is a function of the competitiveness of its industries located in different countries, which necessitates a dual

There are also a number of papers devoted to numerical solution of probabilistic constrained programming (for references see Prekopa [32, 331). In the present paper we

AB far as the parameter ko limits the value of objective function, we will name this method the Method of Constraints. The solution procedure component is a

The social structure of science pro- vides the context for this inquiry into a complex psychosocial process that affects both the reward system and the