Fast discrete Fourier transform on generalized sparse grids
Fast discrete Fourier transform on generalized sparse grids
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03.2013Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11923
Inhalt
In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of dominating mixed smoothness. In particular, we derive estimates for the error and the cost. We construct interpolants with a computational cost complexity which is substantially lower than for the standard full grid case. The associated generalized sparse grid interpolants have the same approximation order as the standard full grid interpolants, provided that certain additional regularity assumptions on the considered functions are fulfilled. 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/10.1007/978-3-319-04537-5_4Reihe, Nummer
INS Preprints ; 1305Griebel, Michael; Hamaekers, Jan: Fast discrete Fourier transform on generalized sparse grids. In: INS Preprints, 1305.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11923
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11923
@unpublished{handle:20.500.11811/11923,
author = {{Michael Griebel} and {Jan Hamaekers}},
title = {Fast discrete Fourier transform on generalized sparse grids},
publisher = {Institut für Numerische Simulation (INS)},
year = 2013,
month = mar,
INS Preprints},
volume = 1305,
note = {In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of dominating mixed smoothness. In particular, we derive estimates for the error and the cost. We construct interpolants with a computational cost complexity which is substantially lower than for the standard full grid case. The associated generalized sparse grid interpolants have the same approximation order as the standard full grid interpolants, provided that certain additional regularity assumptions on the considered functions are fulfilled. Numerical results validate our theoretical findings.},
url = {https://hdl.handle.net/20.500.11811/11923}
}
author = {{Michael Griebel} and {Jan Hamaekers}},
title = {Fast discrete Fourier transform on generalized sparse grids},
publisher = {Institut für Numerische Simulation (INS)},
year = 2013,
month = mar,
INS Preprints},
volume = 1305,
note = {In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of dominating mixed smoothness. In particular, we derive estimates for the error and the cost. We construct interpolants with a computational cost complexity which is substantially lower than for the standard full grid case. The associated generalized sparse grid interpolants have the same approximation order as the standard full grid interpolants, provided that certain additional regularity assumptions on the considered functions are fulfilled. Numerical results validate our theoretical findings.},
url = {https://hdl.handle.net/20.500.11811/11923}
}
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