Sampling inequalities for anisotropic tensor product grids
Sampling inequalities for anisotropic tensor product grids
Dokument öffnen (514.6KB)Datum der Veröffentlichung
04.2018Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
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Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11808
Inhalt
We derive sampling inequalities for discrete point sets which are of anisotropic tensor product form. Such sampling inequalities can be used to prove convergence for arbitrary stable reconstruction processes. As usual in the context of high-dimensional problems, our sampling inequalities are expressed in terms of the number of data sites, i.e. the number of points in the sparse grid. To this end, new bounds on specific monotone sets and on the number of points in an anisotropic sparse grid are derived. High dimensional approximation; anistropic sparse grids; sampling inequalities; kernel-based reconstructions.
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1093/imanum/dry080Reihe, Nummer
INS Preprints ; 1805Rieger, Christian; Wendland, Holger: Sampling inequalities for anisotropic tensor product grids. In: INS Preprints, 1805.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11808
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11808
@unpublished{handle:20.500.11811/11808,
author = {{Christian Rieger} and {Holger Wendland}},
title = {Sampling inequalities for anisotropic tensor product grids},
publisher = {Institut für Numerische Simulation (INS)},
year = 2018,
month = apr,
INS Preprints},
volume = 1805,
note = {We derive sampling inequalities for discrete point sets which are of anisotropic tensor product form. Such sampling inequalities can be used to prove convergence for arbitrary stable reconstruction processes. As usual in the context of high-dimensional problems, our sampling inequalities are expressed in terms of the number of data sites, i.e. the number of points in the sparse grid. To this end, new bounds on specific monotone sets and on the number of points in an anisotropic sparse grid are derived. High dimensional approximation; anistropic sparse grids; sampling inequalities; kernel-based reconstructions.},
url = {https://hdl.handle.net/20.500.11811/11808}
}
author = {{Christian Rieger} and {Holger Wendland}},
title = {Sampling inequalities for anisotropic tensor product grids},
publisher = {Institut für Numerische Simulation (INS)},
year = 2018,
month = apr,
INS Preprints},
volume = 1805,
note = {We derive sampling inequalities for discrete point sets which are of anisotropic tensor product form. Such sampling inequalities can be used to prove convergence for arbitrary stable reconstruction processes. As usual in the context of high-dimensional problems, our sampling inequalities are expressed in terms of the number of data sites, i.e. the number of points in the sparse grid. To this end, new bounds on specific monotone sets and on the number of points in an anisotropic sparse grid are derived. High dimensional approximation; anistropic sparse grids; sampling inequalities; kernel-based reconstructions.},
url = {https://hdl.handle.net/20.500.11811/11808}
}
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