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Scattered Data Modelling Using Radial Basis Functions

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Tutorials on Multiresolution in Geometric Modelling

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

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Abstract

Radial basis functions provide powerful meshless methods for multivariate interpolation from scattered data in arbitrary space dimension. This tutorial first explains the basic features of radial basis function interpolation, including its optimality properties and available error estimates, before critical aspects concerning its stability are discussed. The remainder of this contribution is then devoted to related techniques in scattered data modelling other than plain interpolation. To this end, least squares approximation and multiresolution techniques are explained, and recent progress concerning scattered data filtering is reported.

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Author information

Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Munich, Germany

    Armin Iske

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  1. Armin Iske
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Editors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, 80290, München, Germany

    Armin Iske

  2. SINTEF Applied Mathematics, Postboks 124, Blindern, 0314, Oslo, Norway

    Ewald Quak  & Michael S. Floater  & 

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Iske, A. (2002). Scattered Data Modelling Using Radial Basis Functions. In: Iske, A., Quak, E., Floater, M.S. (eds) Tutorials on Multiresolution in Geometric Modelling. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04388-2_9

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  • DOI: https://doi.org/10.1007/978-3-662-04388-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07819-4

  • Online ISBN: 978-3-662-04388-2

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