Stable splittings of Hilbert spaces of functions of infinitely many variables
Stable splittings of Hilbert spaces of functions of infinitely many variables
Dokument öffnen (461.1KB)Datum der Veröffentlichung
2016Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11846
Inhalt
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings. The construction has been used in an exemplary way for guiding dimension- and scale-adaptive algorithms in application areas such as statistical learning theory, reduced order modeling, and information-based complexity. We prove results on compact embeddings, norm equivalences, and the estimation of ϵ-dimensions. A new condition for the equivalence of weighted ANOVA and anchored norms is also given.
Schlagwörter
Tensor product Hilbert spaces, weighted Hilbert space decompositions, functions of infinitely many variables, epsilon-dimensions, L2 approximation, compact embeddings, high-dimensional model representation
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1016/j.jco.2017.01.003Reihe, Nummer
INS Preprints ; 1617Griebel, Michael; Oswald, Peter: Stable splittings of Hilbert spaces of functions of infinitely many variables. In: INS Preprints, 1617.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11846
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11846
@unpublished{handle:20.500.11811/11846,
author = {{Michael Griebel} and {Peter Oswald}},
title = {Stable splittings of Hilbert spaces of functions of infinitely many variables},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
INS Preprints},
volume = 1617,
note = {We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings. The construction has been used in an exemplary way for guiding dimension- and scale-adaptive algorithms in application areas such as statistical learning theory, reduced order modeling, and information-based complexity. We prove results on compact embeddings, norm equivalences, and the estimation of ϵ-dimensions. A new condition for the equivalence of weighted ANOVA and anchored norms is also given.},
url = {https://hdl.handle.net/20.500.11811/11846}
}
author = {{Michael Griebel} and {Peter Oswald}},
title = {Stable splittings of Hilbert spaces of functions of infinitely many variables},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
INS Preprints},
volume = 1617,
note = {We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings. The construction has been used in an exemplary way for guiding dimension- and scale-adaptive algorithms in application areas such as statistical learning theory, reduced order modeling, and information-based complexity. We prove results on compact embeddings, norm equivalences, and the estimation of ϵ-dimensions. A new condition for the equivalence of weighted ANOVA and anchored norms is also given.},
url = {https://hdl.handle.net/20.500.11811/11846}
}
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