Regularity of irregular subdivision

We study the smoothness of the limit function for one-dimensional unequally spaced interpolating subdivision schemes. The new grid points introduced at every level can lie in irregularly spaced locations between old, adjacent grid points and not only midway as is usually the case. For the natural generalization of the four-point scheme introduced by Dubuc and Dyn, Levin, and Gregory, we show that, under some geometric restrictions, the limit function is always C1; under slightly stronger restrictions we show that the limit function is almost C2, the same regularity as in the regularly spaced case.

Duke Scholars

Author Ingrid Daubechies Mathematics