Convexity preserving interpolatory subdivision schemes

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    Abstract

    We construct local subdivision schemes that interpolate functional univariate data and that preserve convexity. The resulting limit function of these schemes is continuous and convex for arbitrary convex data. Moreover this class of schemes is restricted to a subdivision scheme that generates a limit function that is convex and continuously differentiable for strictly convex data. The approximation order of this scheme is four. Some generalizations, such as tension control and piecewise convexity preservation, are briefly discussed.
    Original languageUndefined
    Article number10.1007/s003659900093
    Pages (from-to)609-630
    Number of pages22
    JournalConstructive approximation
    Volume14
    Issue number4
    DOIs
    Publication statusPublished - 1998

    Keywords

    • Subdivision schemes
    • EWI-16342
    • METIS-140429
    • Interpolation
    • IR-68284
    • Convexity preservation

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