BIT Numerical Mathematics

, Volume 53, Issue 2, pp 545–563 | Cite as

Construction of interpolation splines minimizing semi-norm in \(W_{2}^{(m,m-1)}(0,1)\) space

  • Kholmat M. Shadimetov
  • Abdullo R. Hayotov


In the present paper using S.L. Sobolev’s method interpolation splines minimizing the semi-norm in a Hilbert space are constructed. Explicit formulas for coefficients of interpolation splines are obtained. The obtained interpolation spline is exact for polynomials of degree m−2 and e x . Also some numerical results are presented.


Interpolation spline Hilbert space Norm minimizing property S.L. Sobolev’s method Discrete argument function 

Mathematics Subject Classification (2010)

41A05 41A15 



The authors are very thankful to professor Erich Novak for discussion of the results of this paper. A.R. Hayotov thanks professor Erich Novak and his research group for hospitality.

The final part of this work was done in the Friedrich-Schiller University of Jena, Germany. The second author thanks the DAAD for scholarship. Furthermore the second author also thanks IMU/CDE-program for travel support to the Friedrich-Schiller University of Jena, Germany.

We are very grateful to the Referee for remarks and suggestions, which have improved the quality of this paper.


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Institute of Mathematics and Information TechnologiesUzbek Academy of SciencesTashkentUzbekistan

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