Numerical Algorithms

, Volume 2, Issue 1, pp 39–61 | Cite as

Elementarym-harmonic cardinal B-splines

  • Christophe Rabut


We generalize the notion of B-spline to the thin plate splines and to otherd-dimensional polyharmonic splines as defined in [Duchon, [3]]; for regular nets, we give the main properties of these “B-splines”: Fourier transform, decay when ∥x∥ → ∞, stability, integration property, links between B-splines of different orders or of different dimensions and in particular link with the polynomial B-splines, approximation using B-splines... We show that, in some sense, B-splines may be considered as a regularized form of the Dirac distribution.

Subject classification



B-splines thin plate spline polyharmonic splines radial basis functions quasi-interpolant 


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Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1992

Authors and Affiliations

  • Christophe Rabut
    • 1
  1. 1.Complexe scientifique de RangueilINSA-Centre de MathématiquesToulouse CedexFrance

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