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The Average Size of Certain Gram-Determinants and Interpolation on Non-Compact Sets

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Multivariate Approximation and Splines

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 125))

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Abstract

The determinants of Gram-matrices defined by reproducing kernels can be averaged with respect to the arguments occuring. The results can be used to prove that, in a very general situation, interpolation points exist which furnish small Lagrange elements. The results are complementary to Auerbach’s Theorem. They apply even in cases where interpolation takes place on noncompact sets.

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References

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Author information

Authors and Affiliations

  1. Lehrstuhl für Mathematik III, Universität Dortmund, 44221, Dortmund, Germany

    Manfred Reimer

Authors
  1. Manfred Reimer
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Mannheim, D-68131, Mannheim, Germany

    Günther Nürnberger  & Guido Walz  & 

  2. Institut für Numerische Mathematik, Technische Universität Dresden, D-01062, Dresden, Germany

    Jochen W. Schmidt

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© 1997 Springer Basel AG

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Reimer, M. (1997). The Average Size of Certain Gram-Determinants and Interpolation on Non-Compact Sets. In: Nürnberger, G., Schmidt, J.W., Walz, G. (eds) Multivariate Approximation and Splines. ISNM International Series of Numerical Mathematics, vol 125. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8871-4_19

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  • DOI: https://doi.org/10.1007/978-3-0348-8871-4_19

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9808-9

  • Online ISBN: 978-3-0348-8871-4

  • eBook Packages: Springer Book Archive

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