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On Thin Plate Spline Interpolation

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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 119))

Abstract

We present a simple, PDE-based proof of the result (Math Comput 70(234):719–737, 2001) by Johnson that the error estimates of Duchon (RAIRO Anal Numér 12(4):325–334, 1978) for thin plate spline interpolation can be improved by h 1∕2. We illustrate that \(\mathcal{H}\)-matrix techniques can successfully be employed to solve very large thin plate spline interpolation problems.

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Author information

Authors and Affiliations

  1. Kapsch TrafficCom, Am Europlatz 2, A-1120, Wien, Austria

    M. Löhndorf

  2. Technische Universität Wien, A-1140, Wien, Austria

    J. M. Melenk

Authors
  1. M. Löhndorf
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  2. J. M. Melenk
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Editor information

Editors and Affiliations

  1. School of Mechanical Engineering, University of Campinas, Campinas, Brazil

    Marco L. Bittencourt

  2. Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Ney A. Dumont

  3. EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jan S. Hesthaven

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Löhndorf, M., Melenk, J.M. (2017). On Thin Plate Spline Interpolation. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_32

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