Understanding recurrence relations for Chebyshevian B-splines via blossoms

On real-analytic recurrence relations for cardinal exponential B-splines

Let LN+1 be a linear differential operator of order N + 1 with constant coefficients and real eigenvalues 1, . . . , N+1, let E( N+1) be the space of all C∞-solutions of LN+1 on the real line. We show that for N 2 and n = 2, . . . , N , there is a recurrence relation from suitable subspaces En to En+1 involving real-analytic functions, andwithEN+1=E( N+1) if and only if contiguous eigenvalues a...

Geometrically continuous piecewise quasi Chebyshevian splines

Quasi extended Chebyshev spaces (QEC-spaces for short) represent the largest class of spaces of sufficient regularity which are suitable for design [1]. In particular, they contain the well-known extended Chebyshev spaces as a special instance (and therefore can represent transcendental functions) as well as the so called variable degree polynomial spaces [2], that are very effective in handlin...

A recurrence relation for rational B-splines

In this note a recurrence relation for rational B-splines is presented. Using this formula, it is possible to write a rational spline in terms of normalized rational B-splines of lower order, with certain rational coeecients; these coincide with that generated by the well-known "rational version of the de Boor algorithm" based on knot-insertion Farin '88], Farin '89]. A modiied relation is pres...

The Degree of Approximation by Chebyshevian Splines

This papet studies the connections between the smoothness of a function and its degree of approximation by Chebyshevian splines. This is accomplished by proving companion direct and inverse theorems which give a characterization of smoothness in terms of degree of approximation. A determination of the saturation properties is included.

Asymptotics of Orthogonal Polynomials via Recurrence Relations