Approximation to uniform distribution in SO(3)

Damir Ferizović; Carlos Beltrán

doi:10.1007/s00365-020-09506-1

Approximation to uniform distribution in SO(3)

Titel in Übersetzung: Approximation der Gleichverteilung in SO(3)

Damir Ferizović, Carlos Beltrán^*

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Analysis und Zahlentheorie (5010)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

Abstract

Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO (3) , with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO (3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L ²-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest.

Titel in Übersetzung	Approximation der Gleichverteilung in SO(3)
Originalsprache	englisch
Seiten (von - bis)	283-311
Seitenumfang	29
Fachzeitschrift	Constructive Approximation
Jahrgang	52
Ausgabenummer	2
Frühes Online-Datum	9 Mai 2020
DOIs	https://doi.org/10.1007/s00365-020-09506-1
Publikationsstatus	Veröffentlicht - 1 Okt. 2020

ASJC Scopus subject areas

Computational Mathematics
Analyse
Allgemeine Mathematik

Zugriff auf Dokument

10.1007/s00365-020-09506-1

Andere Dateien und Links

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2 Gastvortrag
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1 Vortrag bei Workshop, Seminar oder Kurs

Approximation to uniform distribution on SO(3)
Damir Ferizović (Redner/in)
26 März 2019
Aktivität: Vortrag oder Präsentation › Gastvortrag › Science to science
Lower Bound of the Discrete Green Energy - Elkies Lemma
Damir Ferizović (Redner/in)
10 Apr. 2019
Aktivität: Vortrag oder Präsentation › Vortrag bei Konferenz oder Fachtagung › Science to science
An Upper Bound for the Green Energy on SO(3)
Damir Ferizović (Redner/in)
19 Sept. 2018
Aktivität: Vortrag oder Präsentation › Gastvortrag › Science to science

Doctoral School Award
Ferizović, Damir (Empfänger/-in), 10 Jan. 2020
Auszeichnung: Preise / Medaillen / Ehrungen

Dieses zitieren

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N2 - Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO (3) , with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO (3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L 2-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest.

AB - Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO (3) , with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on SO (3). The variance of rotation matrices sampled by a certain determinantal point process is estimated, and formulas for the L 2-norm of Gegenbauer polynomials with index 2 are deduced, which might be of independent interest.

KW - Determinantal point processes

KW - Green energy

KW - Point arrangements

KW - Rotation group

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JF - Constructive Approximation

IS - 2

ER -

Approximation to uniform distribution in SO(3)

Abstract

ASJC Scopus subject areas

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Aktivitäten

Approximation to uniform distribution on SO(3)

Lower Bound of the Discrete Green Energy - Elkies Lemma

An Upper Bound for the Green Energy on SO(3)

Auszeichnungen

Doctoral School Award

Dieses zitieren