Convexity preservation of the four-point interpolatory subdivision scheme

In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly convex data, Conditions on the t ension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-poi nt scheme with tension parameter bounded from above by a bound smaller than 1/16, Thus the scheme generates C-1 limit functions and has approximation order two. (C) 1999 Elsevier Science B.V. All rights reserved.