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Modern Developments in Multivariate Approximation pp 143–152Cite as

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Asymptotic Error Expansions for Schoenberg Type Operators

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

Abstract

We derive an asymptotic expansion of the L2-error of scaled Schoenberg operators in terms of powers of the scale parameter. The class of operators includes cardinal interpolation operators, in one or several variables. The polyphase case is also considered. Connections to multiwavelet expansions are inherent, but not worked out here.

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References

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Author information

Authors and Affiliations

  1. Faculty of Applied Mathematics, Technical University of Gdar¨ªsk, Naturowicza 11/12, 80-952, Gdar¨ªsk, Poland

    Karol Dziedziul

  2. Institut f¨¹r Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593, Stuttgart, Germany

    Kurt Jetter

Authors
  1. Karol Dziedziul
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  2. Kurt Jetter
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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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© 2003 Springer Basel AG

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Dziedziul, K., Jetter, K. (2003). Asymptotic Error Expansions for Schoenberg Type Operators. 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_7

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  • DOI: https://doi.org/10.1007/978-3-0348-8067-1_7

  • 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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