USING THE DISCRETE FOURIER-TRANSFORM TO ANALYZE THE CONVERGENCE OF SUBDIVISION SCHEMES

While the continuous Fourier transform is a well-established standard tool for the analysis of subdivision schemes, we present a new techniq ue based on the discrete Fourier transform instead. We first prove a v ery general convergence criterion for arbitrary interpolatory schemes, i.e., for nonstationary, globally supported, or even nonlinear scheme s. Then we use the discrete Fourier transform as an algebraic tool to transform subdivision schemes into a form suitable for the analysis. T his allows us to formulate simple and numerically stable sufficient cr iteria for the convergence of subdivision schemes of very general type . We analyze some example schemes to illustrate the resulting easy-to- apply criteria which merely require to numerically estimate the maximu m of a smooth function on a compact interval. (C) 1998 Academic Press.