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).
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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

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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).