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Matematicheskie Zametki, 2010, Volume 88, Issue 6, Pages 836–844
DOI: https://doi.org/10.4213/mzm6576 (Mi mzm6576) 		 
This article is cited in 20 scientific papers (total in 20 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
Full-text PDF (451 kB) Citations (20)
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DOI: https://doi.org/10.4213/mzm6576
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 $k=0,\dots,4$.
Keywords: cubic spline, shape-preserving interpolation, $k$‑monotonicity, $B$-spline, matrix with diagonal dominance.
Received: 01.11.2008
English version:
Mathematical Notes, 2010, Volume 88, Issue 6, Pages 798–805
DOI: https://doi.org/10.1134/S0001434610110209
Bibliographic databases:
Document Type: Article
UDC: 517.518.8
Language: Russian
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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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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