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Matematicheskie Trudy, 2019, Volume 22, Number 1, Pages 19–67
DOI: https://doi.org/10.33048/mattrudy.2019.22.102
(Mi mt347)
 

This article is cited in 7 scientific papers (total in 7 papers)

Shape-preservation conditions for cubic spline interpolation

V. V. Bogdanovab, Yu. S. Volkovab

a Sobolev Institute of Mathematics, Novosibirsk, 630090 Russia
b Novosibirsk State University, Novosibirsk, 630090 Russia
Full-text PDF (408 kB) Citations (7)
References:
Abstract: We consider the problem on shape-preserving interpolation by classical cubic splines. Namely, we consider conditions guaranteeing that, for a positive function (or a function whose $k$th derivative is positive), the cubic spline (respectively, its $k$th derivative) is positive. We present a survey of known results, completely describe the cases in which boundary conditions are formulated in terms of the first derivative, and obtain similar results for the second derivative. We discuss in detail mathematical methods for obtaining sufficient conditions for shape-preserving interpolation. We also develop such methods, which allows us to obtain general conditions for a spline and its derivative to be positive. We prove that, for a strictly positive function (or a function whose derivative is positive), it is possible to find an interpolant of the same sign as the initial function (respectively, its derivative) by thickening the mesh.
Key words: cubic spline, shape-preserving interpolation, monotonicity, convexity.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0314-2016-0013
The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics, SB RAS (project 0314-2016-0013)
Received: 13.09.2018
Revised: 04.02.2019
Accepted: 27.02.2019
English version:
Siberian Advances in Mathematics, 2019, Volume 29, Issue 4, Pages 231–262
DOI: https://doi.org/10.3103/S1055134419040011
Bibliographic databases:
Document Type: Article
UDC: 519.518.85
Language: Russian
Citation: V. V. Bogdanov, Yu. S. Volkov, “Shape-preservation conditions for cubic spline interpolation”, Mat. Tr., 22:1 (2019), 19–67; Siberian Adv. Math., 29:4 (2019), 231–262
Citation in format AMSBIB
\Bibitem{BogVol19}
\by V.~V.~Bogdanov, Yu.~S.~Volkov
\paper Shape-preservation conditions for cubic spline interpolation
\jour Mat. Tr.
\yr 2019
\vol 22
\issue 1
\pages 19--67
\mathnet{http://mi.mathnet.ru/mt347}
\crossref{https://doi.org/10.33048/mattrudy.2019.22.102}
\transl
\jour Siberian Adv. Math.
\yr 2019
\vol 29
\issue 4
\pages 231--262
\crossref{https://doi.org/10.3103/S1055134419040011}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85076339086}
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  • This publication is cited in the following 7 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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    Abstract page:484
    Full-text PDF :338
    References:44
    First page:11
     
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