Fast approximation of the discrete Gauss transform in higher dimensions
Fast approximation of the discrete Gauss transform in higher dimensions
View/Date of Publication
10.2011Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11959
Abstract
We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares favorably to existing methods especially when it comes to higher dimensions and a broad range of bandwidths. Numerical results with different datasets in up to 62 dimensions demonstrate its performance.
Subjects
Gauss transform, fast approximation algorithms, high-dimensional
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/s10915-012-9626-3Part of Series
INS Preprints ; 1111Griebel, Michael; Wissel, Daniel: Fast approximation of the discrete Gauss transform in higher dimensions. In: INS Preprints, 1111.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11959
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11959
@unpublished{handle:20.500.11811/11959,
author = {{Michael Griebel} and {Daniel Wissel}},
title = {Fast approximation of the discrete Gauss transform in higher dimensions},
publisher = {Institut für Numerische Simulation (INS)},
year = 2011,
month = oct,
INS Preprints},
volume = 1111,
note = {We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares favorably to existing methods especially when it comes to higher dimensions and a broad range of bandwidths. Numerical results with different datasets in up to 62 dimensions demonstrate its performance.},
url = {https://hdl.handle.net/20.500.11811/11959}
}
author = {{Michael Griebel} and {Daniel Wissel}},
title = {Fast approximation of the discrete Gauss transform in higher dimensions},
publisher = {Institut für Numerische Simulation (INS)},
year = 2011,
month = oct,
INS Preprints},
volume = 1111,
note = {We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares favorably to existing methods especially when it comes to higher dimensions and a broad range of bandwidths. Numerical results with different datasets in up to 62 dimensions demonstrate its performance.},
url = {https://hdl.handle.net/20.500.11811/11959}
}
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