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 tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point 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.
|Place of Publication||Enschede|
|Publisher||University of Twente|
|Number of pages||4|
|Publication status||Published - 1998|
|Name||Memorandum Faculteit TW|
- Convexity preservation
- Stationary subdivision scheme