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Trudy Inst. Mat. i Mekh. UrO RAN, 2007, Volume 13, Number 2, Pages 156–166 (Mi timm98)  

This article is cited in 5 scientific papers (total in 5 papers)

Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions

Yu. N. Subbotin


Abstract: In this paper with the help of parabolic splines we construct a linear method of approximate recovery of functions by their values on an arbitrary grid. In the method, a spline inherits the properties of monotonicity and convexity from the approximated function, and is sufficiently smooth. In addition, the constructed linear operator as an operator acting from the space of continuous functions to the same space has the norm equal to one. We also obtain similar results for trigonometric splines of third order.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2007, 259, suppl. 2, S231–S242

Document Type: Article
UDC: 519.65
Received: 12.04.2007

Citation: Yu. N. Subbotin, “Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 2, 2007, 156–166; Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S231–S242

Citation in format AMSBIB
\Bibitem{Sub07}
\by Yu.~N.~Subbotin
\paper Approximations by polynomial and trigonometric splines of third order preserving some properties of approximated functions
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2007
\vol 13
\issue 2
\pages 156--166
\mathnet{http://mi.mathnet.ru/timm98}
\elib{http://elibrary.ru/item.asp?id=12040778}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2007
\vol 259
\issue , suppl. 2
\pages S231--S242
\crossref{https://doi.org/10.1134/S0081543807060168}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38949168215}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Strelkova, V. T. Shevaldin, “Approximation by local $\mathcal L$-splines that are exact on subspaces of the kernel of a differential operator”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S133–S141  mathnet  crossref  isi  elib
    2. E. V. Strelkova, V. T. Shevaldin, “Form preservation under approximation by local exponential splines of an arbitrary order”, Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 171–179  mathnet  crossref  isi  elib
    3. Yu. S. Volkov, E. G. Pytkeev, V. T. Shevaldin, “Orders of approximation by local exponential splines”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 175–184  mathnet  crossref  isi  elib
    4. Yu. S. Volkov, V. T. Shevaldin, “Usloviya formosokhraneniya pri interpolyatsii splainami vtoroi stepeni po Subbotinu i po Marsdenu”, Tr. IMM UrO RAN, 18, no. 4, 2012, 145–152  mathnet  elib
    5. E. V. Strelkova, V. T. Shevaldin, “Local exponential splines with arbitrary knots”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 189–194  mathnet  crossref  mathscinet  isi  elib
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