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On the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines

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Modern Developments in Multivariate Approximation

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

Abstract

This paper proves convergence rates for local scattered data interpolation by polyharmonic splines. To this end, it is shown that the Lagrange basis functions of polyharmonic spline interpolation are invariant under uniform scalings. Consequences of this important result for the numerical stability of the local interpolation scheme are discussed. A stable algorithm for the evaluation of polyharmonic spline interpolants is proposed.

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Author information

Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, D-85747, Garching, Germany

    Armin Iske

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  1. Armin Iske
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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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Iske, A. (2003). On the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines. 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_8

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  • DOI: https://doi.org/10.1007/978-3-0348-8067-1_8

  • 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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