Convexity Preservation of the Four-Point Interpolatory Subdivision Scheme

摘要

In this note the authors examine the convexity preserving properties of the211u001e(linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin 211u001ewhen applied to functional univariate strictly convex data. Conditions on the 211u001etension parameter guaranteeing preservation of convexity are derived.