Classification of Spline Objects

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko


This chapter is special in the sense that it represents a collection of the facts from the previous chapters, which underline the internal unity of these chapters. This is a selective observation which helps us to classify general methods and objects of variational spline theory. The chapter was prepared on the basis of the paper by Bezhaev (1990).


Hilbert Space Operator Equation Variational Theory Spline Interpolation Linear Continuous Operator 
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. Bezhaev, A.Yu. (1984): “The traces of Dm-splines on smooth manifolds”, Preprint No. 113, 14pp. (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]Google Scholar
  2. Bezhaev, A.Yu. (1988): “Splines on manifolds” , in Sov. J. Numer. Math. Modelling, Vol. 2, No. 4, pp. 287–300 (VNU Science Press, Utrecht)Google Scholar
  3. Bezhaev, A.Yu. (1989): “Variational vector spline-functions” , in Proc. of Int. Conf. on Numerical Methods and Applications, pp. 40–46 (Publ. House of Bulgarian Ac. Sci., Sofia)Google Scholar
  4. Bezhaev, A.Yu. (1990): “Methods of variational spline theory” , in Numerical methods and Mathematical Modelling, pp. 3–24 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]Google Scholar
  5. Cui Ming-gen, Zhang Mian, Deng Zhong-xing (1986): “Two-dimensional reproducing kernal and surface spline interpolation” , J. Comput. Math., Vol. 4, No. 2, pp. 177–181Google Scholar
  6. Duchon, J. (1977) :“Splines minimizing rotation-invariant semi-norms in Sobolev spaces”, Lect. Notes in Math., Vol. 571, pp. 85–100 (Springer Verlag)Google Scholar
  7. Freeden, W. (1981): “On spherical spline interpolation and approximation” , Math. Meth. Appl. Sci., Vol. 3, pp. 551–575Google Scholar
  8. Gordon, W.J. (1971): “Blending function methods of bivariate and multivariate interpolation and approximation” , SIAM J. Numer. Anal., Vol. 8, pp. 158–171Google Scholar
  9. Harder, R.L., Desmarais, R.N. (1972): “Interpolation using surface splines”, J. Aircraft., Vol. 9, No. 2, pp. 189–191CrossRefGoogle Scholar
  10. Wahba, G. (1981) :“Spline interpolation and smoothing on the sphere”, SIAM J. Sci. Stat. Comput. Sphere, Vol. 2, pp. 5–16Google Scholar
  11. Wahba, G. (1984): “Surface fitting with scattered noisy data on Euclidean D-space and on the sphere” , Rocky Mountain J. of Math., Vol. 14, No. 1, pp. 281–299Google 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

Personalised recommendations