Analysis of Hermite interpolatory subdivision schemes

The theory of matrix subdivision schemes provides tools for the analysis of general uniform stationary matrix schemes The special case of Hermite interpolatory subdivision schemes deals with re nement algorithms for the function and the derivatives values with matrix masks depending upon the re nement level i e non stationary matrix masks Here we rst show that a Hermite interpolatory subdivision scheme can be transformed into a stationary process Then using special schemes for generating some Hermite type divided di erences we give the theory and the tools for analyzing the convergence and smoothness of Hermite interpolatory schemes Stationary Hermite interpolatory schemes Hermite type subdivision schemes of order were already considered in and in In the present paper we are discussing the basic properties and the proper analysis tools for higher order Hermite type subdivision schemes The analysis presented here is an adaptation of the methods in and especially exploiting the structure and the special signi cance of Hermite type data Examples and numerical implementation of the analysis tools are presented in The Hermite interpolatory scheme of order m is of the form