Advances in Computational Mathematics

, Volume 11, Issue 4, pp 287–314 | Cite as

Multivariate interpolating (m, l, s)-splines

  • A. Bouhamidi
  • A. Le Méhauté

Abstract

The multivariate interpolating (m, l, s)-splines are a natural generalization of Duchon's thin plate splines (TPS). More precisely, we consider the problem of interpolation with respect to some finite number of linear continuous functionals defined on a semi-Hilbert space and minimizing its semi-norm. The (m, l, s)-splines are explicitly given as a linear combination of translates of radial basis functions. We prove the existence and uniqueness of the interpolating (m, l, s)-splines and investigate some of their properties. Finally, we present some practical examples of (m, l, s)-splines for Lagrange and Hermite interpolation.

Hilbert space interpolating splines minimization thin plate splines multiquadric splines radial basis functions 65D05-65D07-65D10 41A15 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • A. Bouhamidi
    • 1
  • A. Le Méhauté
    • 2
  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du Littoral – Côte d'OpaleCalais CedexFrance
  2. 2.Département de Mathématiques, Faculté des Sciences, UniversitéCNRS UMR 6629Nantes CedexFrance

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