Stability of subdivision schemes

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Abstract

The stability of stationary interpolatory subdivision schemes for univariate data is investigated. If the subdivision scheme is linear, its stability follows from the convergence of the scheme, but for nonlinear subdivision schemes one needs stronger conditions and the stability analysis of nonlinear schemes is more involved. Apart from the fact that it is natural to demand that subdivision schemes are stable, it also has an advantage in a theoretical sense: is it shown that the approximation properties of stable schemes can very easily be determined.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages16
ISBN (Print)0169-2690
Publication statusPublished - 1998

Publication series

Name
PublisherDepartment of Applied Mathematics, University of Twente
No.1469
ISSN (Print)0169-2690

Keywords

  • MSC-65D17
  • METIS-141106
  • Subdivision
  • MSC-41A05
  • Stability
  • approximation order
  • Computer aided geometric design
  • EWI-3289
  • IR-65658
  • MSC-65D05

Cite this

Kuijt, F., & van Damme, R. M. J. (1998). Stability of subdivision schemes. Enschede: University of Twente, Department of Applied Mathematics.
Kuijt, F. ; van Damme, Rudolf M.J. / Stability of subdivision schemes. Enschede : University of Twente, Department of Applied Mathematics, 1998. 16 p.
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abstract = "The stability of stationary interpolatory subdivision schemes for univariate data is investigated. If the subdivision scheme is linear, its stability follows from the convergence of the scheme, but for nonlinear subdivision schemes one needs stronger conditions and the stability analysis of nonlinear schemes is more involved. Apart from the fact that it is natural to demand that subdivision schemes are stable, it also has an advantage in a theoretical sense: is it shown that the approximation properties of stable schemes can very easily be determined.",
keywords = "MSC-65D17, METIS-141106, Subdivision, MSC-41A05, Stability, approximation order, Computer aided geometric design, EWI-3289, IR-65658, MSC-65D05",
author = "F. Kuijt and {van Damme}, {Rudolf M.J.}",
note = "Imported from MEMORANDA",
year = "1998",
language = "Undefined",
isbn = "0169-2690",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1469",

}

Kuijt, F & van Damme, RMJ 1998, Stability of subdivision schemes. University of Twente, Department of Applied Mathematics, Enschede.

Stability of subdivision schemes. / Kuijt, F.; van Damme, Rudolf M.J.

Enschede : University of Twente, Department of Applied Mathematics, 1998. 16 p.

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Stability of subdivision schemes

AU - Kuijt, F.

AU - van Damme, Rudolf M.J.

N1 - Imported from MEMORANDA

PY - 1998

Y1 - 1998

N2 - The stability of stationary interpolatory subdivision schemes for univariate data is investigated. If the subdivision scheme is linear, its stability follows from the convergence of the scheme, but for nonlinear subdivision schemes one needs stronger conditions and the stability analysis of nonlinear schemes is more involved. Apart from the fact that it is natural to demand that subdivision schemes are stable, it also has an advantage in a theoretical sense: is it shown that the approximation properties of stable schemes can very easily be determined.

AB - The stability of stationary interpolatory subdivision schemes for univariate data is investigated. If the subdivision scheme is linear, its stability follows from the convergence of the scheme, but for nonlinear subdivision schemes one needs stronger conditions and the stability analysis of nonlinear schemes is more involved. Apart from the fact that it is natural to demand that subdivision schemes are stable, it also has an advantage in a theoretical sense: is it shown that the approximation properties of stable schemes can very easily be determined.

KW - MSC-65D17

KW - METIS-141106

KW - Subdivision

KW - MSC-41A05

KW - Stability

KW - approximation order

KW - Computer aided geometric design

KW - EWI-3289

KW - IR-65658

KW - MSC-65D05

M3 - Report

SN - 0169-2690

BT - Stability of subdivision schemes

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Kuijt F, van Damme RMJ. Stability of subdivision schemes. Enschede: University of Twente, Department of Applied Mathematics, 1998. 16 p.