Zur Konvergenz von Splines

  • Herbert Arndt
  • Bernd Eickenscheidt
Part of the International Series of Numerical Mathematics book series (ISNM, volume 30)


When dealing with interpolation problems with certain nonlinear classes of spline functions, an estimate of the norm of an interpolation operator for linear spline interpolation is needed. If the knots are equally spaced and polynomial splines of degree less than fourteen are used, these norms may be estimated independent of the number of knots. This result is used in [2] to establish existence for nonlinear interpolation problems for sufficiently small mesh size and to obtain optimal convergence.


Interpolation Problem Interpolation Operator Linear Spline Small Mesh Size Nonlinear Classis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ahlberg, J.H., Nilson, E.N., Walsh, J.L.: The Theory of Splines and Their Applications. New York and London, Academic Press 1967zbMATHGoogle Scholar
  2. [2]
    Arndt, H.: Interpolation mit regulären Splines. Erscheint im J. Approximation TheoryGoogle Scholar
  3. [3]
    De Boor, C.: On the Convergence of Odd-Degree Spline Interpolation. J. Approximation Theory 1 (1968), 452–463MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Eickenscheidt, B.: Zur Konvergenz des Randwertproblems bei der Interpolation mit regulären Spline-Funktionen. Diplomarbeit, Münster 1974Google Scholar
  5. [5]
    Karlin, S.: Total Positivity, vol. 1. Stanford University Press 1968Google Scholar
  6. [6]
    Werner, H., Schaback, R.: Praktische Mathematik II. Berlin-Heidelberg-New York, Springer 1972zbMATHGoogle Scholar

Copyright information

© Springer Basel AG 1976

Authors and Affiliations

  • Herbert Arndt
    • 1
  • Bernd Eickenscheidt
    • 2
  1. 1.Institut für Numerische Mathematik der Universität44 MünsterGermany
  2. 2.Rechenzentrum der Universität44 MünsterGermany

Personalised recommendations