Convergence of irregular Hermite subdivision schemes

Yao Zhao; Di Rong Chen

doi:10.1016/j.cagd.2010.02.004

Convergence of irregular Hermite subdivision schemes

Yao Zhao
, Di Rong Chen^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

Abstract

We consider in this paper the convergence of Hermite subdivision schemes related to the irregular grids X. It is reduced to the convergence of a scalar subdivision scheme, so the results concerning perturbation of convergent scalar subdivision schemes are applied. For interpolatory subdivision schemes H_X, with the irregular grid X which is equivalent to the regular grid X^* in a suitable sense, we proved that the convergence of H_X is implied by that of H_X*. Our arguments work in the settings of L_p-convergence and uniform convergence.

Original language	English
Pages (from-to)	372-381
Number of pages	10
Journal	Computer Aided Geometric Design
Volume	27
Issue number	5
DOIs	https://doi.org/10.1016/j.cagd.2010.02.004
State	Published - Jun 2010

Keywords

Associated subdivision scheme
Difference subdivision scheme
Hermite subdivision scheme
Interpolatory subdivision scheme
Irregular grid

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10.1016/j.cagd.2010.02.004

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title = "Convergence of irregular Hermite subdivision schemes",

abstract = "We consider in this paper the convergence of Hermite subdivision schemes related to the irregular grids X. It is reduced to the convergence of a scalar subdivision scheme, so the results concerning perturbation of convergent scalar subdivision schemes are applied. For interpolatory subdivision schemes HX, with the irregular grid X which is equivalent to the regular grid X* in a suitable sense, we proved that the convergence of HX is implied by that of HX*. Our arguments work in the settings of Lp-convergence and uniform convergence.",

keywords = "Associated subdivision scheme, Difference subdivision scheme, Hermite subdivision scheme, Interpolatory subdivision scheme, Irregular grid",

author = "Yao Zhao and Chen, \{Di Rong\}",

year = "2010",

month = jun,

doi = "10.1016/j.cagd.2010.02.004",

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AU - Zhao, Yao

AU - Chen, Di Rong

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N2 - We consider in this paper the convergence of Hermite subdivision schemes related to the irregular grids X. It is reduced to the convergence of a scalar subdivision scheme, so the results concerning perturbation of convergent scalar subdivision schemes are applied. For interpolatory subdivision schemes HX, with the irregular grid X which is equivalent to the regular grid X* in a suitable sense, we proved that the convergence of HX is implied by that of HX*. Our arguments work in the settings of Lp-convergence and uniform convergence.

AB - We consider in this paper the convergence of Hermite subdivision schemes related to the irregular grids X. It is reduced to the convergence of a scalar subdivision scheme, so the results concerning perturbation of convergent scalar subdivision schemes are applied. For interpolatory subdivision schemes HX, with the irregular grid X which is equivalent to the regular grid X* in a suitable sense, we proved that the convergence of HX is implied by that of HX*. Our arguments work in the settings of Lp-convergence and uniform convergence.

KW - Associated subdivision scheme

KW - Difference subdivision scheme

KW - Hermite subdivision scheme

KW - Interpolatory subdivision scheme

KW - Irregular grid

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U2 - 10.1016/j.cagd.2010.02.004

DO - 10.1016/j.cagd.2010.02.004

M3 - 文章

AN - SCOPUS:77951024883

SN - 0167-8396

VL - 27

SP - 372

EP - 381

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 5

ER -

Convergence of irregular Hermite subdivision schemes

Abstract

Keywords

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