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Trudy Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 3, Pages 200–225 (Mi timm1563)  

Extremal functional interpolation and splines

Yu. N. Subbotin, S. I. Novikov, V. T. Shevaldin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: The paper is a survey of the results obtained in the problems of extremal function interpolation over the past 50 years. Various statements of problems in this direction are analyzed both for the case of one variable and for the case of several variables. A special focus is put on the role of interpolation splines of different types (polynomial, interpolating in the mean, $\mathcal{L}$-splines, $m$-harmonic, etc.) in solving the problems of extremal function interpolation. Important applications of the results and methods of extremal interpolation to other problems in approximation theory and the theory of splines are specified.

Keywords: interpolation, splines, approximation, differential operators, difference operators.

DOI: https://doi.org/10.21538/0134-4889-2018-24-3-200-225

Full text: PDF file (366 kB)
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Bibliographic databases:

UDC: 517.5
MSC: 41A15
Received: 20.05.2018

Citation: Yu. N. Subbotin, S. I. Novikov, V. T. Shevaldin, “Extremal functional interpolation and splines”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 3, 2018, 200–225

Citation in format AMSBIB
\Bibitem{SubNovShe18}
\by Yu.~N.~Subbotin, S.~I.~Novikov, V.~T.~Shevaldin
\paper Extremal functional interpolation and splines
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 3
\pages 200--225
\mathnet{http://mi.mathnet.ru/timm1563}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-3-200-225}
\elib{http://elibrary.ru/item.asp?id=35511288}


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