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Numerische Mathematik

, Volume 107, Issue 2, pp 181–211 | Cite as

An extension of a bound for functions in Sobolev spaces, with applications to (m, s)-spline interpolation and smoothing

  • Rémi Arcangéli
  • María Cruz López de Silanes
  • Juan José TorrensEmail author
Article

Abstract

Given a function f on a bounded open subset Ω of \({\mathbb{R}}^n\) with a Lipschitz-continuous boundary, we obtain a Sobolev bound involving the values of f at finitely many points of \(\overline\Omega\) . This result improves previous ones due to Narcowich et al. (Math Comp 74, 743–763, 2005), and Wendland and Rieger (Numer Math 101, 643–662, 2005). We then apply the Sobolev bound to derive error estimates for interpolating and smoothing (m, s)-splines. In the case of smoothing, noisy data as well as exact data are considered.

Mathematics Subject Classification (2000)

41A25 41A05 41A15 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Rémi Arcangéli
    • 1
  • María Cruz López de Silanes
    • 2
  • Juan José Torrens
    • 3
    Email author
  1. 1.ArbasFrance
  2. 2.Departamento de Matemática Aplicada, C.P.S.Universidad de ZaragozaZaragozaSpain
  3. 3.Departamento de Ingeniería Matemática e InformáticaUniversidad Pública de NavarraPamplonaSpain

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