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Shape-preserving interpolation by cubic splines

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    Yu. S. Volkov & V. L. Miroshnichenko

  2. Novosibirsk State University, Novosibirsk, Russia

    Yu. S. Volkov & V. L. Miroshnichenko

  3. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

    V. V. Bogdanov

  4. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    V. T. Shevaldin

Authors
  1. Yu. S. Volkov
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  2. V. V. Bogdanov
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  3. V. L. Miroshnichenko
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  4. V. T. Shevaldin
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Correspondence to Yu. S. Volkov.

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Original Russian Text © Yu. S. Volkov, V. V. Bogdanov, V. L. Miroshnichenko, V. T. Shevaldin, 2010, published in Matematicheskie Zametki, 2010, Vol. 88, No. 6, pp. 836–844.

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Volkov, Y.S., Bogdanov, V.V., Miroshnichenko, V.L. et al. Shape-preserving interpolation by cubic splines. Math Notes 88, 798–805 (2010). https://doi.org/10.1134/S0001434610110209

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  • DOI: https://doi.org/10.1134/S0001434610110209

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