Non-stationary Subdivision Schemes: State of the Art and Perspectives

Costanza Conti; Nira Dyn

doi:10.1007/978-3-030-57464-2_4

Non-stationary Subdivision Schemes: State of the Art and Perspectives

Costanza Conti^*, Nira Dyn

^*Corresponding author for this work

School of Mathematical Sciences

University of Florence

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

14 Scopus citations

Abstract

This paper reviews the state of the art of non-stationary subdivision schemes, which are iterative procedures for generating smooth objects from discrete data, by repeated level dependent linear refinements. In particular the paper emphasises the potentiality of these schemes and the wide perspective they open, in comparison with stationary schemes based on level-independent linear refinements.

Original language	English
Title of host publication	Approximation Theory XVI, 2019
Editors	Gregory E. Fasshauer, Marian Neamtu, Larry L. Schumaker
Publisher	Springer
Pages	39-71
Number of pages	33
ISBN (Print)	9783030574635
DOIs	https://doi.org/10.1007/978-3-030-57464-2_4
State	Published - 2021
Event	International conference on Approximation Theory XVI, 2019 - Nashville, United States Duration: 19 May 2019 → 22 May 2019

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	336
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International conference on Approximation Theory XVI, 2019
Country/Territory	United States
City	Nashville
Period	19/05/19 → 22/05/19

Funding

Funders	Funder number
Indam-GNCS

Keywords

Analysis of convergence/smoothness
Generation/reproduction of exponential polynomials
Linear operators
Non-stationary schemes
Subdivision schemes

Access to Document

10.1007/978-3-030-57464-2_4

Cite this

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title = "Non-stationary Subdivision Schemes: State of the Art and Perspectives",

abstract = "This paper reviews the state of the art of non-stationary subdivision schemes, which are iterative procedures for generating smooth objects from discrete data, by repeated level dependent linear refinements. In particular the paper emphasises the potentiality of these schemes and the wide perspective they open, in comparison with stationary schemes based on level-independent linear refinements.",

keywords = "Analysis of convergence/smoothness, Generation/reproduction of exponential polynomials, Linear operators, Non-stationary schemes, Subdivision schemes",

author = "Costanza Conti and Nira Dyn",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; International conference on Approximation Theory XVI, 2019 ; Conference date: 19-05-2019 Through 22-05-2019",

year = "2021",

doi = "10.1007/978-3-030-57464-2_4",

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Conti, C & Dyn, N 2021, Non-stationary Subdivision Schemes: State of the Art and Perspectives. in GE Fasshauer, M Neamtu & LL Schumaker (eds), Approximation Theory XVI, 2019. Springer Proceedings in Mathematics and Statistics, vol. 336, Springer, pp. 39-71, International conference on Approximation Theory XVI, 2019, Nashville, United States, 19/05/19. https://doi.org/10.1007/978-3-030-57464-2_4

Non-stationary Subdivision Schemes: State of the Art and Perspectives. / Conti, Costanza; Dyn, Nira.
Approximation Theory XVI, 2019. ed. / Gregory E. Fasshauer; Marian Neamtu; Larry L. Schumaker. Springer, 2021. p. 39-71 (Springer Proceedings in Mathematics and Statistics; Vol. 336).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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KW - Generation/reproduction of exponential polynomials

KW - Linear operators

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Non-stationary Subdivision Schemes: State of the Art and Perspectives

Abstract

Publication series

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Keywords

Access to Document

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