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Quadratic/linear rational spline histopolation

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Abstract

The histopolation with quadratic/linear rational splines of class \(C^2\) is studied. Such kind of splines keep the sign of its second derivative on the whole interval and, consequently, the given histogram should be strictly convex or strictly concave. The grid points of the histogram and suitable number of the spline knots between them are supposed to place arbitrarily. The uniqueness of such an histopolant is established. It is shown that the histopolant may not exist but some sufficient conditions for the existence are given. Presented numerical results confirm their adequacy.

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Acknowledgements

The research was supported by institutional research funding IUT20-57 of the Estonian Ministry of Education and Research.

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Authors and Affiliations

  1. Tallinn University of Technology, Tallinn, Estonia

    Helle Hallik

  2. Tartu University, Tartu, Estonia

    Peeter Oja

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  1. Helle Hallik
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  2. Peeter Oja
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Correspondence to Helle Hallik.

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Communicated by Tom Lyche.

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Hallik, H., Oja, P. Quadratic/linear rational spline histopolation. Bit Numer Math 57, 629–648 (2017). https://doi.org/10.1007/s10543-017-0645-1

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  • DOI: https://doi.org/10.1007/s10543-017-0645-1

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