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Fast Discrete Fourier Transform on Generalized Sparse Grids

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Sparse Grids and Applications - Munich 2012

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 97))

Abstract

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.

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Acknowledgements

This work was supported in part by the Collaborative Research Centre 1060 of the Deutsche Forschungsgemeinschaft.

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Authors and Affiliations

  1. Institute for Numerical Simulation, University of Bonn, Wegelerstr. 6, 53115, Bonn, Germany

    Michael Griebel

  2. Fraunhofer Institute for Algorithms and Scientific Computing SCAI, Schloss Birlinghoven, 53754, Sankt Augustin, Germany

    Jan Hamaekers

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  1. Michael Griebel
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  2. Jan Hamaekers
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Correspondence to Jan Hamaekers .

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Editors and Affiliations

  1. Institut für Numerische Simulation, Universität Bonn, Bonn, Germany

    Jochen Garcke

  2. Institute for Parallel and Distributed Systems, Universität Stuttgart, Stuttgart, Germany

    Dirk Pflüger

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Griebel, M., Hamaekers, J. (2014). Fast Discrete Fourier Transform on Generalized Sparse Grids. In: Garcke, J., Pflüger, D. (eds) Sparse Grids and Applications - Munich 2012. Lecture Notes in Computational Science and Engineering, vol 97. Springer, Cham. https://doi.org/10.1007/978-3-319-04537-5_4

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