Sparse representation of multivariate functions based on discrete point evaluations
Sparse representation of multivariate functions based on discrete point evaluations
![Open Access](/xmlui/themes/Fakultaeten//images/32px-Open_Access_logo_PLoS_white.svg.png)
Autor
Byrenheid, Glenn
Art der Hochschulschrift
DissertationPrüfungsdatum
09.11.2018Datum der Veröffentlichung
22.01.2019Erstgutachter
Ullrich, TinoZweitgutachter
Griebel, MichaelBeteiligte Institutionen
Rheinische Friedrich-Wilhelms-Universität BonnMetadaten
Zur Langanzeige
Zitierbare Links ![Bitte verwenden Sie für Zitate oder Verweise einen der angegebenen persistenten Identifikatoren und nicht die in der Adresszeile Ihres Webbrowser angezeigte URL.](/xmlui/themes/Fakultaeten//images/info-circle.svg)
Inhalt
Functions provide one of the most important building blocks for model descriptions of reality. Central point of this thesis is the approximation of multivariate functions using Faber-Schauder hat functions. In the first part we describe mixed smoothness Sobolev-Besov-Triebel-Lizorkin spaces by decreasing properties of Faber-Schauder coefficients. This allows us to provide equivalent norm representations based on discrete function values. In the second part we apply this theory to study sparse grid sampling or more generally the problem of sampling recovery for Sobolev classes (especially with integrability $pneq 2$). We provide new convergence estimates for a Faber-Schauder based sparse grid method measuring errors in $L_{q}([0,1]^d)$ with $p
Schlagwörter
Abtastalgorithmen, Dünngitterapproximation, Funktionenräume, Faber-Schauder-Basen, Sobolev-Räume, Besov-Räume, Triebel-Lizorkin-Räume, Sampling, Nichtlineare Approximation, Beste m-Term-Approximation, sampling representations, sampling, sparse grid approximation, function spaces, Faber-Schauder bases, Sobolev spaces, Besov spaces, Triebel-Lizorkin spaces, nonlinear approximation, best m-term approximation, greedy methods
Klassifikation (DDC)
510 MathematikByrenheid, Glenn: Sparse representation of multivariate functions based on discrete point evaluations. - Bonn, 2019. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-53130
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-53130
@phdthesis{handle:20.500.11811/7838,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-53130,
author = {{Glenn Byrenheid}},
title = {Sparse representation of multivariate functions based on discrete point evaluations},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2019,
month = jan,
note = {Functions provide one of the most important building blocks for model descriptions of reality. Central point of this thesis is the approximation of multivariate functions using Faber-Schauder hat functions. In the first part we describe mixed smoothness Sobolev-Besov-Triebel-Lizorkin spaces by decreasing properties of Faber-Schauder coefficients. This allows us to provide equivalent norm representations based on discrete function values. In the second part we apply this theory to study sparse grid sampling or more generally the problem of sampling recovery for Sobolev classes (especially with integrability $pneq 2$). We provide new convergence estimates for a Faber-Schauder based sparse grid method measuring errors in $L_{q}([0,1]^d)$ with $p
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-53130,
author = {{Glenn Byrenheid}},
title = {Sparse representation of multivariate functions based on discrete point evaluations},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2019,
month = jan,
note = {Functions provide one of the most important building blocks for model descriptions of reality. Central point of this thesis is the approximation of multivariate functions using Faber-Schauder hat functions. In the first part we describe mixed smoothness Sobolev-Besov-Triebel-Lizorkin spaces by decreasing properties of Faber-Schauder coefficients. This allows us to provide equivalent norm representations based on discrete function values. In the second part we apply this theory to study sparse grid sampling or more generally the problem of sampling recovery for Sobolev classes (especially with integrability $pneq 2$). We provide new convergence estimates for a Faber-Schauder based sparse grid method measuring errors in $L_{q}([0,1]^d)$ with $p
url = {https://hdl.handle.net/20.500.11811/7838}
}
E-Dissertationen: Verwandte Dokumente
Anzeige der Dokumente mit ähnlichem Titel, Autor, Urheber und Thema.
-
On Approximability of Bounded Degree Instances of Selected Optimization Problems
Schmied, Richard (2013-08-07)In order to cope with the approximation hardness of an underlying optimization problem, it is advantageous to consider specific families of instances with properties that can be exploited to obtain efficient approximation ... -
On Discrete and Geometric Firefighting
Schwarzwald, Barbara Anna (2021-08-19)Wildfires ravaging forests around the globe cost lives, homes and billions in damages every year, which motivates the study of effective firefighting. In the area of theoretical computer science, several different models ... -
An Application of Kolmogorov's Superposition Theorem to Function Reconstruction in Higher Dimensions
Braun, Jürgen (2009-12-01)In this thesis we present a Regularization Network approach to reconstruct a continuous function ƒ:[0,1]<sup>n</sup>→<b>R</b> from its function values ƒ(<b>x</b><sub>j</sub>) on discrete data points <b>x</b><sub>j</sub>, ...