Interpolation lattices for hyperbolic cross trigonometric polynomials
DC Element | Wert | Sprache |
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dc.contributor.author | Kaemmerer, Lutz | |
dc.contributor.author | Kunis, Stefan | |
dc.contributor.author | Potts, Daniel | |
dc.date.accessioned | 2021-12-23T16:18:18Z | - |
dc.date.available | 2021-12-23T16:18:18Z | - |
dc.date.issued | 2012 | |
dc.identifier.issn | 0885064X | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/12622 | - |
dc.description.abstract | Sparse grid discretisations allow for a severe decrease in the number of degrees of freedom for high-dimensional problems. Recently, the corresponding hyperbolic cross fast Fourier transform has been shown to exhibit numerical instabilities already for moderate problem sizes. In contrast to standard sparse grids as spatial discretisation, we propose the use of oversampled lattice rules known from multivariate numerical integration. This allows for the highly efficient and perfectly stable evaluation and reconstruction of trigonometric polynomials using only one ordinary FFT. Moreover, we give numerical evidence that reasonable small lattices exist such that our new method outperforms the sparse grid based hyperbolic cross FFT for realistic problem sizes. (C) 2011 Elsevier Inc. All rights reserved. | |
dc.description.sponsorship | German Research FoundationGerman Research Foundation (DFG) [KU 2557/1-1]; Helmholtz AssociationHelmholtz Association [VH-NG-526]; The authors thank the referees for their valuable suggestions and gratefully acknowledge support by the German Research Foundation within the project KU 2557/1-1 and by the Helmholtz Association within the young investigator group VH-NG-526. | |
dc.language.iso | en | |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | |
dc.relation.ispartof | JOURNAL OF COMPLEXITY | |
dc.subject | Computer Science | |
dc.subject | Computer Science, Theory & Methods | |
dc.subject | Fast Fourier transform | |
dc.subject | FOURIER-TRANSFORM | |
dc.subject | Hyperbolic cross | |
dc.subject | Lattice rule | |
dc.subject | Mathematics | |
dc.subject | Mathematics, Applied | |
dc.subject | RULES | |
dc.subject | Sparse grid | |
dc.subject | SPARSE GRIDS | |
dc.subject | Trigonometric approximation | |
dc.title | Interpolation lattices for hyperbolic cross trigonometric polynomials | |
dc.type | journal article | |
dc.identifier.doi | 10.1016/j.jco.2011.05.002 | |
dc.identifier.isi | ISI:000298620500006 | |
dc.description.volume | 28 | |
dc.description.issue | 1 | |
dc.description.startpage | 76 | |
dc.description.endpage | 92 | |
dc.contributor.orcid | 0000-0003-3651-4364 | |
dc.contributor.researcherid | AAW-1584-2020 | |
dc.identifier.eissn | 10902708 | |
dc.publisher.place | 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA | |
dcterms.isPartOf.abbreviation | J. Complex. | |
dcterms.oaStatus | Bronze, Green Submitted | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | KuSt212 | - |
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