Convexity preservation of the four-point interpolatory subdivision scheme

Nira Dyn, F. Kuijt, David Levin, Rudolf M.J. van Damme

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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.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversiteit Twente
    Number of pages4
    Publication statusPublished - 1998

    Publication series

    NameMemorandum Faculteit TW
    PublisherUniversiteit Twente
    No.1457

    Keywords

    • MSC-41A29
    • METIS-141108
    • IR-30468
    • Convexity preservation
    • MSC-65D17
    • EWI-3277
    • Stationary subdivision scheme
    • MSC-65D05
    • MSC-41A05

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