On the construction of sparse tensor product spaces
On the construction of sparse tensor product spaces
Dokument öffnen (339.4KB)Datum der Veröffentlichung
05.2011Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11939
Inhalt
Let Ω1 ⊂ ℝn1 and Ω2 ⊂ ℝn2 be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial exactness r1and r2, respectively. In this paper, we study the optimal construction of sparse tensor products made from these spaces. In particular, we derive the resulting cost complexities to approximate functions with anisotropic and isotropic smoothness on the tensor product domain Ω1 × Ω2. Numerical results validate our theoretical findings.
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1090/S0025-5718-2012-02638-XReihe, Nummer
INS Preprints ; 1104Griebel, Michael; Harbrecht, Helmut: On the construction of sparse tensor product spaces. In: INS Preprints, 1104.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11939
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11939
@unpublished{handle:20.500.11811/11939,
author = {{Michael Griebel} and {Helmut Harbrecht}},
title = {On the construction of sparse tensor product spaces},
publisher = {Institut für Numerische Simulation (INS)},
year = 2011,
month = may,
INS Preprints},
volume = 1104,
note = {Let Ω1 ⊂ ℝn1 and Ω2 ⊂ ℝn2 be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial exactness r1and r2, respectively. In this paper, we study the optimal construction of sparse tensor products made from these spaces. In particular, we derive the resulting cost complexities to approximate functions with anisotropic and isotropic smoothness on the tensor product domain Ω1 × Ω2. Numerical results validate our theoretical findings.},
url = {https://hdl.handle.net/20.500.11811/11939}
}
author = {{Michael Griebel} and {Helmut Harbrecht}},
title = {On the construction of sparse tensor product spaces},
publisher = {Institut für Numerische Simulation (INS)},
year = 2011,
month = may,
INS Preprints},
volume = 1104,
note = {Let Ω1 ⊂ ℝn1 and Ω2 ⊂ ℝn2 be two given domains and consider on each domain a multiscale sequence of ansatz spaces of polynomial exactness r1and r2, respectively. In this paper, we study the optimal construction of sparse tensor products made from these spaces. In particular, we derive the resulting cost complexities to approximate functions with anisotropic and isotropic smoothness on the tensor product domain Ω1 × Ω2. Numerical results validate our theoretical findings.},
url = {https://hdl.handle.net/20.500.11811/11939}
}
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