Sparse representation of multivariate functions based on discrete point evaluations
Sparse representation of multivariate functions based on discrete point evaluations
dc.contributor.advisor | Ullrich, Tino | |
dc.contributor.author | Byrenheid, Glenn | |
dc.date.accessioned | 2020-04-26T08:53:23Z | |
dc.date.available | 2020-04-26T08:53:23Z | |
dc.date.issued | 22.01.2019 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/7838 | |
dc.description.abstract | 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 | |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Abtastalgorithmen | |
dc.subject | Dünngitterapproximation | |
dc.subject | Funktionenräume | |
dc.subject | Faber-Schauder-Basen | |
dc.subject | Sobolev-Räume | |
dc.subject | Besov-Räume | |
dc.subject | Triebel-Lizorkin-Räume | |
dc.subject | Sampling | |
dc.subject | Nichtlineare Approximation | |
dc.subject | Beste m-Term-Approximation | |
dc.subject | sampling representations | |
dc.subject | sampling | |
dc.subject | sparse grid approximation | |
dc.subject | function spaces | |
dc.subject | Faber-Schauder bases | |
dc.subject | Sobolev spaces | |
dc.subject | Besov spaces | |
dc.subject | Triebel-Lizorkin spaces | |
dc.subject | nonlinear approximation | |
dc.subject | best m-term approximation | |
dc.subject | greedy methods | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Sparse representation of multivariate functions based on discrete point evaluations | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5n-53130 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 5313 | |
ulbbnediss.date.accepted | 09.11.2018 | |
ulbbnediss.institute | Mathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Institut für Numerische Simulation (INS) | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Griebel, Michael |
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