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Piecewise Chebyshevian splines: interpolation versus design

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Abstract

We consider the wide class of all piecewise Chebyshevian splines with connection matrices at the knots. We prove that a spline space of this class is “good for interpolation” if and only if the spline space obtained by integration is “good for design”. As a consequence, this provides us with a simple practical description of all such spline spaces which can be used for solving Hermite interpolation problems. These results strongly rely on the properties of blossoms.

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Authors and Affiliations

  1. Laboratoire Jean Kuntzmann, Université Grenoble-Alpes, BP53, Cedex 9, 38041, Grenoble, France

    Marie-Laurence Mazure

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  1. Marie-Laurence Mazure
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Correspondence to Marie-Laurence Mazure.

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Mazure, ML. Piecewise Chebyshevian splines: interpolation versus design. Numer Algor 77, 1213–1247 (2018). https://doi.org/10.1007/s11075-017-0360-7

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  • DOI: https://doi.org/10.1007/s11075-017-0360-7

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