Approximation by Positive Definite Kernels

  • Robert Schaback
  • Holger Wendland
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 142)


This contribution extends earlier work [16] on interpolation/approximation by positive definite basis functions in several aspects. First, it works out the relations between various types of kernels in more detail and more generality. Second, it uses the new generality to exhibit the first example of a discontinuous positive definite function. Third, it establishes the first link from (radial) basis function theory to n-widths, and finally it uses this link to prove quasi–optimality results for approximation rates of interpolation processes and decay rates for eigenvalues of integral operators having smooth kernels.


Radial Basis Function Integral Operator Native Space Positive Definite Function Positive Definite Kernel 
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Copyright information

© Birkhäuser Verlag Basel 2002

Authors and Affiliations

  • Robert Schaback
    • 1
  • Holger Wendland
    • 1
  1. 1.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenGermany

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