Hermite-interpolatory subdivision schemes

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Abstract

Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness conditions known from the literature are discussed. In order to allow a simpler construction of suitable nonlinear Hermite subdivision schemes, these conditions are posed as assumptions. For linear Hermite subdivision, explicit schemes that satisfy sufficient conditions for $C^2$-convergence are constructed. This leads to larger classes of $C^2$ schemes than known from the literature. Finally, convexity preserving Hermite-interpolatory subdivision is examined, and some explicit rational schemes that generate $C^1$ limit functions are presented.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversiteit Twente
Number of pages17
Publication statusPublished - 1998

Publication series

NameMemorandum Faculteit TW
PublisherUniversiteit Twente
No.1461

Keywords

  • MSC-41A05
  • MSC-65D05
  • stationary linear subdivision
  • Stationary non-linear subdivision
  • MSC-65D17
  • Hermite interpolation
  • Convexity preservation
  • IR-30467
  • METIS-141107
  • MSC-41A29
  • EWI-3281

Cite this

Kuijt, F., & van Damme, R. M. J. (1998). Hermite-interpolatory subdivision schemes. (Memorandum Faculteit TW; No. 1461). Enschede: Universiteit Twente.
Kuijt, F. ; van Damme, Rudolf M.J. / Hermite-interpolatory subdivision schemes. Enschede : Universiteit Twente, 1998. 17 p. (Memorandum Faculteit TW; 1461).
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abstract = "Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness conditions known from the literature are discussed. In order to allow a simpler construction of suitable nonlinear Hermite subdivision schemes, these conditions are posed as assumptions. For linear Hermite subdivision, explicit schemes that satisfy sufficient conditions for $C^2$-convergence are constructed. This leads to larger classes of $C^2$ schemes than known from the literature. Finally, convexity preserving Hermite-interpolatory subdivision is examined, and some explicit rational schemes that generate $C^1$ limit functions are presented.",
keywords = "MSC-41A05, MSC-65D05, stationary linear subdivision, Stationary non-linear subdivision, MSC-65D17, Hermite interpolation, Convexity preservation, IR-30467, METIS-141107, MSC-41A29, EWI-3281",
author = "F. Kuijt and {van Damme}, {Rudolf M.J.}",
note = "Imported from MEMORANDA",
year = "1998",
language = "Undefined",
series = "Memorandum Faculteit TW",
publisher = "Universiteit Twente",
number = "1461",

}

Kuijt, F & van Damme, RMJ 1998, Hermite-interpolatory subdivision schemes. Memorandum Faculteit TW, no. 1461, Universiteit Twente, Enschede.

Hermite-interpolatory subdivision schemes. / Kuijt, F.; van Damme, Rudolf M.J.

Enschede : Universiteit Twente, 1998. 17 p. (Memorandum Faculteit TW; No. 1461).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Hermite-interpolatory subdivision schemes

AU - Kuijt, F.

AU - van Damme, Rudolf M.J.

N1 - Imported from MEMORANDA

PY - 1998

Y1 - 1998

N2 - Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness conditions known from the literature are discussed. In order to allow a simpler construction of suitable nonlinear Hermite subdivision schemes, these conditions are posed as assumptions. For linear Hermite subdivision, explicit schemes that satisfy sufficient conditions for $C^2$-convergence are constructed. This leads to larger classes of $C^2$ schemes than known from the literature. Finally, convexity preserving Hermite-interpolatory subdivision is examined, and some explicit rational schemes that generate $C^1$ limit functions are presented.

AB - Stationary interpolatory subdivision schemes for Hermite data that consist of function values and first derivatives are examined. A general class of Hermite-interpolatory subdivision schemes is proposed, and some of its basic properties are stated. The goal is to characterise and construct certain classes of nonlinear (and linear) Hermite schemes. For linear Hermite subdivision, smoothness conditions known from the literature are discussed. In order to allow a simpler construction of suitable nonlinear Hermite subdivision schemes, these conditions are posed as assumptions. For linear Hermite subdivision, explicit schemes that satisfy sufficient conditions for $C^2$-convergence are constructed. This leads to larger classes of $C^2$ schemes than known from the literature. Finally, convexity preserving Hermite-interpolatory subdivision is examined, and some explicit rational schemes that generate $C^1$ limit functions are presented.

KW - MSC-41A05

KW - MSC-65D05

KW - stationary linear subdivision

KW - Stationary non-linear subdivision

KW - MSC-65D17

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KW - Convexity preservation

KW - IR-30467

KW - METIS-141107

KW - MSC-41A29

KW - EWI-3281

M3 - Report

T3 - Memorandum Faculteit TW

BT - Hermite-interpolatory subdivision schemes

PB - Universiteit Twente

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Kuijt F, van Damme RMJ. Hermite-interpolatory subdivision schemes. Enschede: Universiteit Twente, 1998. 17 p. (Memorandum Faculteit TW; 1461).