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Numerical Algorithms

, Volume 77, Issue 4, pp 1213–1247 | Cite as

Piecewise Chebyshevian splines: interpolation versus design

  • Marie-Laurence Mazure
Original Paper

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.

Keywords

Piecewise Chebyshevian splines Connection matrices Spline Hermite interpolation Schoenberg-Whitney conditions Total positivity (Piecewise) Generalised derivatives B-spline-type bases Knot insertion Blossoms 

Mathematics Subject Classification (2010)

41A05 65D05 65D07 65D17 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Laboratoire Jean KuntzmannUniversité Grenoble-AlpesGrenobleFrance

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