Elementarym-harmonic cardinal B-splines

  title={Elementarym-harmonic cardinal B-splines},
  author={Christophe Rabut},
  journal={Numerical Algorithms},
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… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 15 references

Polyharmonic cardinal splines, Journal of Approximation Theory 60, No. 2 (Febr

Wally R. Madych, S. A. Nelson
View 5 Excerpts
Highly Influenced

Radial basis functions methods for multivariate approximation

Ian Robert Hart Jackson
View 4 Excerpts
Highly Influenced

Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces

Jean Duchon
RAIRO Analyse Numrrique 10, no • 1976
View 5 Excerpts
Highly Influenced

High level m - harmonic cardinal B - splines "

P. S. Laurent, A. Le Mrhaut, L. L. Schumaker
" B - splines polyharmoniques cardinales : Interpolation , quasi - interpolation , filtrage " , Th ~ se d ' Etat , Universit 6 de Toulouse , 1990 . b . " How to build quasi - interpolants . Application to polyharmonic B - splines " , Zurves and Surfaces • 1991

B-splines polyharmoniques cardinales: Interpolation, quasi-interpolation, filtrage", Th~se d'Etat

Christophe Rabut a
Universit6 de Toulouse, • 1990

Madych and S . A . Nelson , Polyharmonic cardinal splines

R Wally
Journal of Approximation Theory • 1990

Ondelettes, analyses multi-rrsolutions et traitement num6rique du signal, Th~se, Universit6

Albert Cohen
Paris IX Dauphine, • 1990
View 2 Excerpts

Multivariate interpolation with radial basis functions, University of Cambridge, DAMPT 1988/NA8

Martin D. Buhmann
View 2 Excerpts

Iterative solution of systems originating from integral equations and surface interpolation, SIAM

Nira Dyn, David Levin
Numerical Analysis 20, • 1983
View 2 Excerpts

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