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Dimension elevation for Chebyshevian splines

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Abstract

Dimension elevation refers to the Chebyshevian version of the classical degree elevation process for polynomials or polynomial splines. In this paper, we consider the case of splines. The original spline space is based on a given Extended Chebsyhev space \({\mathbb{E}}\) contained in another Extended Chebsyhev space \({\mathbb{E}}^*\) of dimension increased by one. The original spline space, based on \({\mathbb{E}}\), is then embedded in a larger one, based on \(\mathbb{E}^*\). Thanks to blossoms we show how to compute the new poles of any spline in the original spline space in terms of its initial poles.

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  1. Laboratoire Jean Kuntzmann, Université Joseph Fourier, BP53, 38041, Grenoble Cedex 9, 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. Dimension elevation for Chebyshevian splines. Numer Algor 56, 1–16 (2011). https://doi.org/10.1007/s11075-010-9369-x

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  • DOI: https://doi.org/10.1007/s11075-010-9369-x

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