Analysis of tensor approximation schemes for continuous functions
Analysis of tensor approximation schemes for continuous functions
Dokument öffnen (426.1KB)Datum der Veröffentlichung
03.2019Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11804
Inhalt
In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an isotropic Sobolev space and discuss the cost when approximating this function in the continuous analogue of the Tucker tensor format or of the tensor train format. We especially show that the cost of both approximations are dimension-robust when the Sobolev space under consideration provides appropriate dimension weights.
Schlagwörter
Tensor format, Approximation error, Rank complexity, Sobolev space with dimension weights
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1007/s10208-021-09544-6Reihe, Nummer
INS Preprints ; 1903Michael Griebel; Helmut Harbrecht: Analysis of tensor approximation schemes for continuous functions. In: INS Preprints, 1903.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11804
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11804
@unpublished{handle:20.500.11811/11804,
author = {{ } and { }},
title = {Analysis of tensor approximation schemes for continuous functions},
publisher = {Institut für Numerische Simulation (INS)},
year = 2019,
month = mar,
INS Preprints},
volume = 1903,
note = {In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an isotropic Sobolev space and discuss the cost when approximating this function in the continuous analogue of the Tucker tensor format or of the tensor train format. We especially show that the cost of both approximations are dimension-robust when the Sobolev space under consideration provides appropriate dimension weights.},
url = {https://hdl.handle.net/20.500.11811/11804}
}
author = {{ } and { }},
title = {Analysis of tensor approximation schemes for continuous functions},
publisher = {Institut für Numerische Simulation (INS)},
year = 2019,
month = mar,
INS Preprints},
volume = 1903,
note = {In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an isotropic Sobolev space and discuss the cost when approximating this function in the continuous analogue of the Tucker tensor format or of the tensor train format. We especially show that the cost of both approximations are dimension-robust when the Sobolev space under consideration provides appropriate dimension weights.},
url = {https://hdl.handle.net/20.500.11811/11804}
}
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