On interpolatory subdivision from approximating subdivision scheme

This paper deals with some theoretical analysis of one strategy for deducing interpolatory from approximating subdivision scheme. First, we derive the explicit formula for one class of interpolatory subdivision schemes deduced from approximating subdivision schemes. This explicit formula paves a way for systematic analysis of interpolatory subdivisions derived by the strategy. We analyze the polynomial generation property of interpolatory subdivision derived by the strategy. Moreover, the explicit formula also has the merit of providing a method for designing new interpolatory and approximating subdivisions, and some new subdivision schemes are constructed.