Hermite B-Splines: n-Refinability and Mask Factorization

Abstract

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute the refinement mask of the Hermite B-splines of any order and in the case of a general scaling factor. Our procedure is solely derived from the polynomial reproduction properties satisfied by Hermite splines and it does not require the explicit construction or evaluation of the basis functions. The second part of the paper discusses the factorization properties of the Hermite B-spline masks in terms of the augmented Taylor operator, which is shown to be the minimal annihilator for the space of discrete monomial Hermite sequences of a fixed degree. All our results can be of use, in particular, in the context of Hermite subdivision schemes and multi-wavelets.

Preface to the Special Issue “Mathematical Modeling in Industrial Engineering and Electrical Engineering”—Special Issue Book

“…The paper authored by M. Cotronei and C. Moosmueller [21] proposes a new development of the Hermite polynomial splines through a quick procedure for the calculation of the refinement mask of the Hermite B-spline of any order and in the case of a general scaling factor. The procedure was derived from the polynomial reproduction properties satisfied by the Hermite splines without requiring the explicit construction/evaluation of the basic functions.…”