Numerical Algorithms

, Volume 10, Issue 2, pp 401–419 | Cite as

Convolution kernels based on thin-plate splines

  • J. Levesley
Article

Abstract

Quasi-interpolation using radial basis functions has become a popular method for constructing approximations to continuous functions in many space dimensions. In this paper we discuss a procedure for generating kernels for quasi-interpolation, using functions which have series expansions involving terms likerα logr. It is shown that such functions are suitable if and only if α is a positive even integer and the spatial dimension is also even.

Keywords

Radial basis functions thin-plate splines convolution kernels 

AMS(MOS) subject classification

41A30 41A63 

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Copyright information

© J.C. Baltzer AG, Science Publishers 1995

Authors and Affiliations

  • J. Levesley
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of LeicesterLeicesterUK

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