Convexity preservation of the four-point interpolatory subdivision scheme

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

    Research output: Book/ReportReportProfessional

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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

    Cite this

    Dyn, N., Kuijt, F., Levin, D., & van Damme, R. M. J. (1998). Convexity preservation of the four-point interpolatory subdivision scheme. (Memorandum Faculteit TW; No. 1457). Enschede: Universiteit Twente.
    Dyn, Nira ; Kuijt, F. ; Levin, David ; van Damme, Rudolf M.J. / Convexity preservation of the four-point interpolatory subdivision scheme. Enschede : Universiteit Twente, 1998. 4 p. (Memorandum Faculteit TW; 1457).
    @book{c09a3be6064c4c3bb5cf3573a13b610a,
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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.",
    keywords = "MSC-41A29, METIS-141108, IR-30468, Convexity preservation, MSC-65D17, EWI-3277, Stationary subdivision scheme, MSC-65D05, MSC-41A05",
    author = "Nira Dyn and F. Kuijt and David Levin and {van Damme}, {Rudolf M.J.}",
    note = "Imported from MEMORANDA",
    year = "1998",
    language = "Undefined",
    series = "Memorandum Faculteit TW",
    publisher = "Universiteit Twente",
    number = "1457",

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    Dyn, N, Kuijt, F, Levin, D & van Damme, RMJ 1998, Convexity preservation of the four-point interpolatory subdivision scheme. Memorandum Faculteit TW, no. 1457, Universiteit Twente, Enschede.

    Convexity preservation of the four-point interpolatory subdivision scheme. / Dyn, Nira; Kuijt, F.; Levin, David; van Damme, Rudolf M.J.

    Enschede : Universiteit Twente, 1998. 4 p. (Memorandum Faculteit TW; No. 1457).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - Convexity preservation of the four-point interpolatory subdivision scheme

    AU - Dyn, Nira

    AU - Kuijt, F.

    AU - Levin, David

    AU - van Damme, Rudolf M.J.

    N1 - Imported from MEMORANDA

    PY - 1998

    Y1 - 1998

    N2 - 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.

    AB - 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.

    KW - MSC-41A29

    KW - METIS-141108

    KW - IR-30468

    KW - Convexity preservation

    KW - MSC-65D17

    KW - EWI-3277

    KW - Stationary subdivision scheme

    KW - MSC-65D05

    KW - MSC-41A05

    M3 - Report

    T3 - Memorandum Faculteit TW

    BT - Convexity preservation of the four-point interpolatory subdivision scheme

    PB - Universiteit Twente

    CY - Enschede

    ER -

    Dyn N, Kuijt F, Levin D, van Damme RMJ. Convexity preservation of the four-point interpolatory subdivision scheme. Enschede: Universiteit Twente, 1998. 4 p. (Memorandum Faculteit TW; 1457).