Blossoming beyond Extended Chebyshev Spaces Original Research Article

In a previous series of papers a theory of blossoming was developed for spaces of functions on an interval I spanned by the constant functions and functions Φ1, …, Φn, where Φ′1, …, Φ′n span an extended Chebyshev space. This theory was then used to construct a generalisation of the Bernstein basis and the de Casteljau algorithm. Also considered were functions defined to be piecewise in such spaces, leading to generalisations of B-splines and the de Boor algorithm. Here we relax the condition that Φ′1, …, Φ′n span an extended Chebyshev space, while retaining all the nice properties of the earlier theory. This allows us to include a large variety of new spaces, including spaces of polynomials which have been found to be successful for tension methods for shape-preserving interpolation.