Splines in Hilbert Spaces

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko


The aim of this chapter is to introduce the main definitions in the abstract variational spline theory and to describe the basic properties of interpolating, smoothing, and mixed abstract splines.


Hilbert Space Null Space Variational Theory Mesh Point Smoothing Spline 
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  1. Anselone, P.M., Laurent, P.-J. (1968): “A general method for the construction of interpolating or smoothing spline function” , in Numer. Math. Vol. 12, No. 1, pp. 66–82MathSciNetzbMATHCrossRefGoogle Scholar
  2. Atteia, M. (1965): “Généralisation de la definition et des properties des ’spline function ’” , in Comp. Rend, Vol. 260, pp. 3550–3553MathSciNetzbMATHGoogle Scholar
  3. Laurent, P.-J. (1973): “Approximation et Optimization” (Dunod, Paris)Google Scholar
  4. Morozov, V.A. (1974): “Regular Methods for the Solution of Incorrect Problems” (Moscow State Univ. Press, Moscow) [in Russian]Google Scholar
  5. Vasilenko, V.A. (1978): “Theory of Spline Functions” (Novosibirsk State Univ. Press, Nobosibirsk) [in Russian]Google Scholar
  6. Vasilenko, V.A. (1983) :“Spline Functions: Theory, Algorithms, Programs” (Nauka, Novosibirsk) [in Russian]zbMATHGoogle Scholar
  7. Vasilenko, V.A., Zuzin, M.V., Kovalkov, A.V. (1984): “Spline Functions and Digital Filters” (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]zbMATHGoogle Scholar
  8. Vasilenko, V.A. (1986): “Spline Functions: Theory, Algorithms, Programs” (Optimization Software, New York)Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko
    • 1
  1. 1.Institute of Computational Mathematics and Mathematical GeophysicsNovosibirskRussia

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