Generalized sparse grid interpolation based on the fast discrete Fourier transform
Generalized sparse grid interpolation based on the fast discrete Fourier transform
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03.2019Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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https://hdl.handle.net/20.500.11811/11805
Abstract
In [9], an algorithm for trigonometric interpolation involving only so-called standard information of multivariate functions on generalized sparse grids has been suggested and a study on its application for the interpolation of functions in periodic Sobolev spaces of dominating mixed smoothness has been presented. In this complementary paper, we now give a slight modification of the proofs, which yields an extension from the pairing (ℋs, ℋtmix) to the more general pairing (ℋs, ℋt,rmix) and which in addition results in an improved estimate for the interpolation error. The improved (constructive) upper bound is in particular consistent with the lower bound for sampling on regular sparse grids with r = 0 and s = 0 given in [4, 5].
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/978-3-030-81362-8_3Part of Series
INS Preprints ; 1902Michael Griebel; Jan Hamaekers: Generalized sparse grid interpolation based on the fast discrete Fourier transform. In: INS Preprints, 1902.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11805
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11805
@unpublished{handle:20.500.11811/11805,
author = {{ } and { }},
title = {Generalized sparse grid interpolation based on the fast discrete Fourier transform},
publisher = {Institut für Numerische Simulation (INS)},
year = 2019,
month = mar,
INS Preprints},
volume = 1902,
note = {In [9], an algorithm for trigonometric interpolation involving only so-called standard information of multivariate functions on generalized sparse grids has been suggested and a study on its application for the interpolation of functions in periodic Sobolev spaces of dominating mixed smoothness has been presented. In this complementary paper, we now give a slight modification of the proofs, which yields an extension from the pairing (ℋs, ℋtmix) to the more general pairing (ℋs, ℋt,rmix) and which in addition results in an improved estimate for the interpolation error. The improved (constructive) upper bound is in particular consistent with the lower bound for sampling on regular sparse grids with r = 0 and s = 0 given in [4, 5].},
url = {https://hdl.handle.net/20.500.11811/11805}
}
author = {{ } and { }},
title = {Generalized sparse grid interpolation based on the fast discrete Fourier transform},
publisher = {Institut für Numerische Simulation (INS)},
year = 2019,
month = mar,
INS Preprints},
volume = 1902,
note = {In [9], an algorithm for trigonometric interpolation involving only so-called standard information of multivariate functions on generalized sparse grids has been suggested and a study on its application for the interpolation of functions in periodic Sobolev spaces of dominating mixed smoothness has been presented. In this complementary paper, we now give a slight modification of the proofs, which yields an extension from the pairing (ℋs, ℋtmix) to the more general pairing (ℋs, ℋt,rmix) and which in addition results in an improved estimate for the interpolation error. The improved (constructive) upper bound is in particular consistent with the lower bound for sampling on regular sparse grids with r = 0 and s = 0 given in [4, 5].},
url = {https://hdl.handle.net/20.500.11811/11805}
}
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