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Mat. Zametki, 2010, Volume 88, Issue 6, Pages 836–844 (Mi mz6576)  

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

Shape-Preserving Interpolation by Cubic Splines

Yu. S. Volkovab, V. V. Bogdanova, V. L. Miroshnichenkoab, V. T. Shevaldinc

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Novosibirsk State University
c Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We consider the problem of shape-preserving interpolation by cubic splines. We propose a unified approach to the derivation of sufficient conditions for the $k$‑monotonicity of splines (the preservation of the sign of any derivative) in interpolation of $k$-monotone data for $k=0,…,4$.

Keywords: cubic spline, shape-preserving interpolation, $k$‑monotonicity, $B$-spline, matrix with diagonal dominance

DOI: https://doi.org/10.4213/mzm6576

Full text: PDF file (451 kB)
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English version:
Mathematical Notes, 2010, 88:6, 798–805

Bibliographic databases:

Document Type: Article
UDC: 517.518.8
Received: 01.11.2008

Citation: Yu. S. Volkov, V. V. Bogdanov, V. L. Miroshnichenko, V. T. Shevaldin, “Shape-Preserving Interpolation by Cubic Splines”, Mat. Zametki, 88:6 (2010), 836–844; Math. Notes, 88:6 (2010), 798–805

Citation in format AMSBIB
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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. Yu. S. Volkov, E. V. Strelkova, V. T. Shevaldin, “Local approximation by splines with displacement of nodes”, Siberian Adv. Math., 23:1 (2013), 69–75  mathnet  crossref  mathscinet  elib
    2. 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
    3. V. V. Bogdanov, “Sufficient conditions for the nonnegativity of solutions to a system of equations with a nonstrictly jacobian matrix”, Siberian Math. J., 54:3 (2013), 425–430  mathnet  crossref  mathscinet  isi
    4. V. V. Bogdanov, Yu. S. Volkov, “Ob usloviyakh formosokhraneniya pri interpolyatsii parabolicheskimi splainami po Subbotinu”, Tr. IMM UrO RAN, 22, no. 4, 2016, 102–113  mathnet  crossref  mathscinet  elib
    5. A.-R. K. Ramazanov, V. G. Magomedova, “Ob usloviyakh vypuklosti splainov po trekhtochechnym ratsionalnym interpolyantam”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 1–6  mathnet  crossref
    6. V. A. Skorospelov, P. A. Turuk, “Geometric support of numerical simulation of flow in the region of the hydroturbine spiral case”, J. Appl. Industr. Math., 12:2 (2018), 355–361  mathnet  crossref  crossref  elib  elib
    7. A.-R. K. Ramazanov, V. G. Magomedova, “Kovypuklaya interpolyatsiya splainami po trekhtochechnym ratsionalnym interpolyantam”, Tr. IMM UrO RAN, 24, no. 3, 2018, 164–175  mathnet  crossref  elib
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