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Multivariate Anisotropic Interpolation on the Torus

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Approximation Theory XIV: San Antonio 2013

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 83))

Abstract

We investigate the error of periodic interpolation, when sampling a function on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix conditions to an anisotropic setting and provide an upper bound for the error of interpolation. These conditions and the investigation of the error especially take different levels of smoothness along certain directions into account.

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Acknowledgments

We thank both the anonymous reviewers for their valuable remarks which improved the presentation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, University Kaiserslautern, Paul-Ehrlich-Straße 31, D-67663, Kaiserslautern, Germany

    Ronny Bergmann

  2. Institute of Mathematics, University of Lübeck, Ratzeburger Allee 160, D-23562, Lübeck, Germany

    Jürgen Prestin

Authors
  1. Ronny Bergmann
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  2. Jürgen Prestin
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Corresponding author

Correspondence to Ronny Bergmann .

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Editors and Affiliations

  1. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois, USA

    Gregory E. Fasshauer

  2. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Bergmann, R., Prestin, J. (2014). Multivariate Anisotropic Interpolation on the Torus. In: Fasshauer, G., Schumaker, L. (eds) Approximation Theory XIV: San Antonio 2013. Springer Proceedings in Mathematics & Statistics, vol 83. Springer, Cham. https://doi.org/10.1007/978-3-319-06404-8_3

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