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Reconstructing Multivariate Functions from Large Data Sets

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Modern Developments in Multivariate Approximation

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 145))

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Abstract

In this paper we discuss an efficient method for reconstructing multivariate functions from large sets of scattered data. Our method is based on (conditionally) positive definite kernels and a partition of unity. It is tailored to solve such reconstruction problems efficiently even if the space dimension is high and the number of data points is huge. We generalize the classical interpolation approach to dealing with other information than point evaluations. Finally, we demonstrate the generality of our approach by providing three different examples.

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Author information

Authors and Affiliations

  1. Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Lotzestr. 16-18, D-37083, Göttingen, Germany

    Holger Wendland

Authors
  1. Holger Wendland
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Gerhard-Mercator-Universität Duisburg, 47048, Duisburg, Germany

    Werner Haussmann

  2. Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, 70593, Stuttgart, Germany

    Kurt Jetter

  3. Fachbereich Mathematik, Universität Dortmund, 44221, Dortmund, Germany

    Manfred Reimer  & Joachim Stöckler  & 

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Wendland, H. (2003). Reconstructing Multivariate Functions from Large Data Sets. In: Haussmann, W., Jetter, K., Reimer, M., Stöckler, J. (eds) Modern Developments in Multivariate Approximation. International Series of Numerical Mathematics, vol 145. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8067-1_17

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  • DOI: https://doi.org/10.1007/978-3-0348-8067-1_17

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9427-2

  • Online ISBN: 978-3-0348-8067-1

  • eBook Packages: Springer Book Archive

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