Contents Invited conferences 3

Hermite subdivision algorithms are mainly designed to interpolate functional values and associated derivatives. These schemes process non-scalar data (functional values and derivatives), and can be rewritten as non-stationary vector algorithms, although their non-stationarity is of a very specific kind. In this talk we present new families of approximating subdivision schemes derived from interpolatory Hermite schemes via the so-called DeRham technique. This allows us to define vector subdivision schemes capable of generating smoother limit functions than the corresponding interpolatory Hermite subdivision schemes starting from the same initial (vector) data. These approximating schemes are dual in the sense that, at each iteration, two new points are inserted in between two old ones. In the analysis of these dual Hermite schemes, we will pay particular attention to their vector-valued nature and we will establish their convergence/smoothness properties via classical techniques of vector subdivision analysis. This is a joint work with Jean-Louis Merrien (INSA Rennes, France) and Lucia Romani (University of Milano-Bicocca, Italy).