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Convexity preservation of the four-point interpolatory subdivision scheme

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Dyn, Nira and Kuijt, Frans and Levin, David and Damme van, Ruud (1998) Convexity preservation of the four-point interpolatory subdivision scheme. [Report]

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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 $C^1$ limit functions and has approximation order two.
Item Type:Report
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/30468
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Metis ID: 141108