Numerical Algorithms

, Volume 77, Issue 4, pp 1213–1247

# Piecewise Chebyshevian splines: interpolation versus design

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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