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Matematicheskie Trudy, 2011, Volume 14, Number 2, Pages 3–13 (Mi mt213)  
This article is cited in 4 scientific papers (total in 4 papers)

Sufficient conditions for the comonotone interpolation of cubic $C^2$

V. V. Bogdanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Full-text PDF (178 kB) Citations (4)
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Abstract: We consider the problem of interpolation of a function under the condition of the preservation of the nature of its piecewise monotonicity. We give sufficient conditions for the comonotone interpolation by a classical cubic $C^2$-spline in the representation based on the expansion of its first derivative in a basis consisting of $B$-splines. These conditions allow to determine whether the soobtained spline is comonotone without solving the interpolation problem.
Key words: comonotone interpolation, cubic spline, matrix of monotone type, $B$-spline.
Received: 12.05.2011
English version:
Siberian Advances in Mathematics, 2012, Volume 22, Issue 3, Pages 153–160
DOI: https://doi.org/10.3103/S1055134412030017
Bibliographic databases:
Document Type: Article
UDC: 519.65
Language: Russian
Citation: V. V. Bogdanov, “Sufficient conditions for the comonotone interpolation of cubic $C^2$”, Mat. Tr., 14:2 (2011), 3–13; Siberian Adv. Math., 22:3 (2012), 153–160
Citation in format AMSBIB
\Bibitem{Bog11}
\by V.~V.~Bogdanov
\paper Sufficient conditions for the comonotone interpolation of cubic $C^2$
\jour Mat. Tr.
\yr 2011
\vol 14
\issue 2
\pages 3--13
\mathnet{http://mi.mathnet.ru/mt213}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2961766}
\transl
\jour Siberian Adv. Math.
\yr 2012
\vol 22
\issue 3
\pages 153--160
\crossref{https://doi.org/10.3103/S1055134412030017}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    Full-text PDF :110
    References:68
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