Piecewise Chebyshevian Splines: Interpolation versus Design
Résumé
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.