On the Structure of Kergin Interpolation for Points in General Position

  • Len Bos
  • Shayne Waldron
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 137)

Abstract

For n+1 points in ℝd, in general position, the Kergin polynomial interpolant of C n functions may be extended to an interpolant of C d−1functions. This results in an explicit set of reduced Kergin functionals naturally stratified by their dependence on certain directional derivatives of order k,0 ≤ kd−1. We show that the polynomials dual to the functionals depending on derivatives of order k are multi-ridge functions of d−k variables and moreover, that the polynomials dual to the purely interpolating functionals(k =0)are always harmonic.

Keywords

General Position Point Evaluation Directional Derivative Lagrange Interpolation Harmonic Polynomial 
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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • Len Bos
    • 1
  • Shayne Waldron
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgary, AlbertaCanada
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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