Splines in Subspaces

  • Anatoly Yu. Bezhaev
  • Vladimir A. Vasilenko


In the previous chapters we have already discussed the main theoretical questions concerning characterization formulae and convergence of variational splines. It is obvious now that there are certain numerical difficulties that arise in the construction and applications of the variational splines (for example, of multi-dimensional D m-splines on the scattered meshes) .


Variational Theory Finite Element Space Interpolation Condition Discontinuity Line Linear Algebraic System 
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  1. Bezhaev, A. Yu., Vasilenko, V.A. (1987): “Splines in the Hilbert spaces and their finite element approximations” , in Sov. J. Numer. Math. Modelling, Vol. 2, No. 3, pp. 191–202 (VNU Science Press, Utrecht)MathSciNetzbMATHGoogle Scholar
  2. De Boor, C. (1978): “A Practical Guide to Splines” , Applied Math. Sciences, No. 27 (Springer Verlag)zbMATHCrossRefGoogle Scholar
  3. Vasilenko, V.A. (1974): “Smoothing splines on subspaces and theorems of compactness” , in Chislennye metody mekhaniki sploshnoy sredi, Vol. 5, No. 5, pp. 37–42 (Ins. Theor. and Appl. Mech. Press, Novosibirsk) [in Russian]MathSciNetGoogle Scholar
  4. Vasilenko, V.A. (1976): “Finite-dimensional approximation in least squared method” , in Variatsionno-raznostnye methody v matematicheskoy fizike, pp. 160–172 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]Google Scholar
  5. Vasilenko, V.A. (1976): “Additional smoothness of spline-interpolants” , Preprint No. 24 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]Google Scholar
  6. Vasilenko, V.A. (1978): “Numerical solution of prolongation problems by finite element method” , in Proc. of All-Union Conference on Finite Element Methods in Math. Physics, pp. 142–148 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]Google Scholar
  7. Vasilenko, V.A. (1978): “Theory of Spline Functions” (Novosibirsk State Univ. Press, Novosibirsk) [in Russian]Google Scholar
  8. Vasilenko, V.A. (1986) :“Spline Functions: Theory, Algorithms, Programs” (Optimization Software, New York)Google Scholar
  9. 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
  10. Vasilenko, V.A. (1984): “Error estimates in FEM for approximation of non-polynomial Dm-splines” , in Metod konechnykh elementov v nekotorikh zadachakh chislennogo analiza, pp. 21–30 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]Google Scholar
  11. Vasilenko, V.A. (1986): “The finite element approximation of minimal surfaces” , in Vistas in Applied Mathematics: Numerical Analysis, Atmospheric Sciences, Immunology, pp. 181–189, (Optimization Software, New York)Google Scholar
  12. Vasilenko, V.A., Rozhenko, A.J. (1989): “Discontinuity localization and spline approximation of discontinuous functions at the scattered meshes” , in Proc. of Int. Conf. on Numerical Methods and Applications, pp. 540–544 (Publ. House of Bulgarian Ac. Sci., Sofia)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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