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Sufficient conditions for the comonotone interpolation of cubic C 2-splines

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    V. V. Bogdanov

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  1. V. V. Bogdanov
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Correspondence to V. V. Bogdanov.

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Original Russian Text © V. V. Bogdanov, 2011, published in Matematicheskie Trudy, 2011, Vol. 14, No. 2, pp. 3–13.

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Bogdanov, V.V. Sufficient conditions for the comonotone interpolation of cubic C 2-splines. Sib. Adv. Math. 22, 153–160 (2012). https://doi.org/10.3103/S1055134412030017

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  • DOI: https://doi.org/10.3103/S1055134412030017

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