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doi:10.1016/S0167-8396(99)00019-9 
Copyright © 1999 Elsevier Science B.V. All rights reserved.
Convexity preservation of the four-point interpolatory subdivision scheme
Received 1 August 1998;
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Abstract
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 C1 limit functions and has approximation order two.
Author Keywords: Stationary subdivision schemes; Convexity preservation
1 Much of this work has been done during a visit of the second author to Tel-Aviv University in March 1998, which was financially supported by Tel-Aviv University and the Dutch Technology Foundation STW.
Corresponding author; email: vandamme@math.utwente.nl
