Analysis and Convergence of Hermite Subdivision Schemes

Hermite interpolation property is desired in applied and computational mathematics. vector subdivision schemes are of interest CAGD for generating curves mathematics building wavelets to numerically solve partial differential equations. In contrast well-studied scalar schemes, employ matrix-valued masks input data, which make their analysis much more complicated difficult than counterparts. Under the spectral condition or chain, through factorization has been extensively studied literature sufficient conditions have given convergence contractivity derived schemes. We contribute study from a different perspective by investigating operators acting on polynomials establishing connections among cascade algorithms, refinable functions. This approach allows us characterize construct all explain chain literature, smoothness using provide simple factorizations normal form such that scheme convergent if only its contractive. also constructively prove there always exist arbitrarily smooth whose basis functions splines linearly independent shifts. Several examples with short support high presented illustrate results this paper.