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Matematicheskie Zametki, 1976, Volume 19, Issue 2, Pages 165–178 (Mi mzm7736)  

This article is cited in 3 scientific papers (total in 3 papers)

A necessary condition for convergence of interpolating parabolic and cubic splines

N. L. Zmatrakov

Institute of Mathematics of the Ural Scientific Center of the USSR Academy of Sciences
Full-text PDF (632 kB) Citations (3)
Abstract: Let the sequence of nets Δn be such that limnmaxih(n)i=0, where h(n)i are the lengths of the segments of a net. The bound max|ij|=1h(n)ih(n)j1αR< is necessary in order that interpolating parabolic and cubic splines converge for any function in C(α=0) or Cα(0<α<1), where Cα is the class of functions satisfying a Lipschitz condition of order α. It is also shown that this bound cannot essentially be weakened.
Received: 10.03.1975
English version:
Mathematical Notes, 1976, Volume 19, Issue 2, Pages 100–107
DOI: https://doi.org/10.1007/BF01098740
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: N. L. Zmatrakov, “A necessary condition for convergence of interpolating parabolic and cubic splines”, Mat. Zametki, 19:2 (1976), 165–178; Math. Notes, 19:2 (1976), 100–107
Citation in format AMSBIB
\Bibitem{Zma76}
\by N.~L.~Zmatrakov
\paper A~necessary condition for convergence of interpolating parabolic and cubic splines
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 2
\pages 165--178
\mathnet{http://mi.mathnet.ru/mzm7736}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=463759}
\zmath{https://zbmath.org/?q=an:0332.41007|0325.41006}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 2
\pages 100--107
\crossref{https://doi.org/10.1007/BF01098740}
Linking options:
  • https://www.mathnet.ru/eng/mzm7736
  • https://www.mathnet.ru/eng/mzm/v19/i2/p165
    Erratum
    This publication is cited in the following 3 articles:
    1. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Cubic spline interpolation of functions with high gradients in boundary layers”, Comput. Math. Math. Phys., 57:1 (2017), 7–25  mathnet  crossref  crossref  isi  elib
    2. I. A. Blatov, A. I. Zadorin, E. V. Kitaeva, “Parabolic spline interpolation for functions with large gradient in the boundary layer”, Siberian Math. J., 58:4 (2017), 578–590  mathnet  crossref  crossref  isi  elib  elib
    3. Yu. S. Volkov, Yu. N. Subbotin, “50 years to Schoenberg's problem on the convergence of spline interpolation”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 222–237  mathnet  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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