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A condition of Schoenberg-Whitney type for multivariate spline interpolation

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Abstract

Lagrange interpolation by finite-dimensional spaces of multivariate spline functions defined on a polyhedral regionK in ℝk is studied. A condition of Schoenberg-Whitney type is introduced. The main result of this paper shows that this condition characterizes all configurationsT inK such that in every neighborhood ofT inK there must exist a configuration\(\tilde T\) which admits unique Lagrange interpolation.

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Authors and Affiliations

  1. Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt, D-85071, Eichstätt, Germany

    Manfred Sommer

  2. Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, D-91058, Erlangen, Germany

    Hans Strauss

Authors
  1. Manfred Sommer
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  2. Hans Strauss
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Communicated by M. Gasca

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Sommer, M., Strauss, H. A condition of Schoenberg-Whitney type for multivariate spline interpolation. Adv Comput Math 5, 381–397 (1996). https://doi.org/10.1007/BF02124752

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  • DOI: https://doi.org/10.1007/BF02124752

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