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Ukrainian Mathematical Journal

, Volume 43, Issue 1, pp 54–58 | Cite as

Behavior of the derivatives of the error of a spline interpolation

  • N. P. Korneichuk
Article

Abstract

Assertions are proved clarifying the character of the behavior of the derivatives of the error of interpolation of differentiable periodic functions by splines with respect to the corresponding derivatives of the standard perfect spline determining the error on the entire class of functions.

Keywords

Periodic Function Spline Interpolation Entire Class Differentiable Periodic Function Perfect Spline 
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.

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Literature cited

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    J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York (1967).Google Scholar
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    S. B. Stechkin and Yu. N. Subbotin, Splines in Computational Mathematics [in Russian], Nauka, Moscow (1976).Google Scholar
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    N. P. Korneichuk, “On approximation of functions and their derivatives by interpolation splines,” Dokl. Akad. Nauk SSSR,264, No. 5, 1063–1066 (1982).Google Scholar
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    N. P. Korneichuk, Splines in Approximation Theory [in Russian], Nauka, Moscow (1984).Google Scholar
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    N. P. Korneichuk, “On approximation of differentiable functions and their derivatives by parabolic splines,” Ukr. Mat. Zh.,35, No. 6, 702–710 (1983).Google Scholar
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    N. P. Korneichuk, “Some sharp inequalities for differentiable functions and an estimate of the approximation of functions and their derivatives by interpolation cubic splines,” Sib. Mat. Zh.,34, No. 5, 94–108 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • N. P. Korneichuk
    • 1
  1. 1.Institute of MathematicsAcademy of Sciences of the Ukrainian SSRKiev

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