A New Method for the Analysis of Univariate Nonuniform Subdivision Schemes

Nira Dyn; David Levin; Jungho Yoon

doi:10.1007/s00365-014-9247-1

A New Method for the Analysis of Univariate Nonuniform Subdivision Schemes

Nira Dyn, David Levin, Jungho Yoon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

This paper presents a new method for the analysis of convergence and smoothness of univariate nonuniform subdivision schemes. The analysis involves ideas from the theory of asymptotically equivalent subdivision schemes and nonuniform Laurent polynomial representation together with a new perturbation result. Application of the new method is presented for the analysis of interpolatory subdivision schemes based upon extended Chebyshev systems and for a class of smoothly varying schemes.

Original language	English
Pages (from-to)	173-188
Number of pages	16
Journal	Constructive Approximation
Volume	40
Issue number	2
DOIs	https://doi.org/10.1007/s00365-014-9247-1
State	Published - Oct 2014

Bibliographical note

Funding Information:
This work was supported by Basic Science Research Program 2012R1A1A2004518 and Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

Asymptotic equivalence
Extended Chebyshev system
Laurent polynomial
Nonuniform subdivision
Smoothly varying scheme

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10.1007/s00365-014-9247-1

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title = "A New Method for the Analysis of Univariate Nonuniform Subdivision Schemes",

abstract = "This paper presents a new method for the analysis of convergence and smoothness of univariate nonuniform subdivision schemes. The analysis involves ideas from the theory of asymptotically equivalent subdivision schemes and nonuniform Laurent polynomial representation together with a new perturbation result. Application of the new method is presented for the analysis of interpolatory subdivision schemes based upon extended Chebyshev systems and for a class of smoothly varying schemes.",

keywords = "Asymptotic equivalence, Extended Chebyshev system, Laurent polynomial, Nonuniform subdivision, Smoothly varying scheme",

author = "Nira Dyn and David Levin and Jungho Yoon",

note = "Funding Information: This work was supported by Basic Science Research Program 2012R1A1A2004518 and Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

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AU - Levin, David

AU - Yoon, Jungho

N1 - Funding Information: This work was supported by Basic Science Research Program 2012R1A1A2004518 and Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology Publisher Copyright: © 2014, Springer Science+Business Media New York.

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N2 - This paper presents a new method for the analysis of convergence and smoothness of univariate nonuniform subdivision schemes. The analysis involves ideas from the theory of asymptotically equivalent subdivision schemes and nonuniform Laurent polynomial representation together with a new perturbation result. Application of the new method is presented for the analysis of interpolatory subdivision schemes based upon extended Chebyshev systems and for a class of smoothly varying schemes.

AB - This paper presents a new method for the analysis of convergence and smoothness of univariate nonuniform subdivision schemes. The analysis involves ideas from the theory of asymptotically equivalent subdivision schemes and nonuniform Laurent polynomial representation together with a new perturbation result. Application of the new method is presented for the analysis of interpolatory subdivision schemes based upon extended Chebyshev systems and for a class of smoothly varying schemes.

KW - Asymptotic equivalence

KW - Extended Chebyshev system

KW - Laurent polynomial

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KW - Smoothly varying scheme

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A New Method for the Analysis of Univariate Nonuniform Subdivision Schemes

Abstract

Bibliographical note

Keywords

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