Analysis of univariate nonstationary subdivision schemes with application to gaussian-based interpolatory schemes

Nira Dyn; David Levin; Jungho Yoon

doi:10.1137/050638217

Analysis of univariate nonstationary subdivision schemes with application to gaussian-based interpolatory schemes

Nira Dyn, David Levin, Jungho Yoon

Department of Mathematics

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

23 Scopus citations

Abstract

This paper is concerned with nonstationary subdivision schemes. First, we derive new sufficient conditions for C smoothness of such schemes. Next, a new class of interpolatory 2m-point nonstationary subdivision schemes based on Gaussian interpolation is presented. These schemes are shown to be C ^L+μ with L ∈ ℤ₊ and μ ∈ (0, 1), where L is the integer smoothness order of the known 2m-point Deslauriers-Dubuc interpolatory schemes.

Original language	English
Pages (from-to)	470-488
Number of pages	19
Journal	SIAM Journal on Mathematical Analysis
Volume	39
Issue number	2
DOIs	https://doi.org/10.1137/050638217
State	Published - 2007

Keywords

Asymptotical equivalence
Gaussian
Interpolation
Nonstationary subdivision
Radial basis function

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10.1137/050638217

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abstract = "This paper is concerned with nonstationary subdivision schemes. First, we derive new sufficient conditions for C smoothness of such schemes. Next, a new class of interpolatory 2m-point nonstationary subdivision schemes based on Gaussian interpolation is presented. These schemes are shown to be C L+μ with L ∈ ℤ+ and μ ∈ (0, 1), where L is the integer smoothness order of the known 2m-point Deslauriers-Dubuc interpolatory schemes.",

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AB - This paper is concerned with nonstationary subdivision schemes. First, we derive new sufficient conditions for C smoothness of such schemes. Next, a new class of interpolatory 2m-point nonstationary subdivision schemes based on Gaussian interpolation is presented. These schemes are shown to be C L+μ with L ∈ ℤ+ and μ ∈ (0, 1), where L is the integer smoothness order of the known 2m-point Deslauriers-Dubuc interpolatory schemes.

KW - Asymptotical equivalence

KW - Gaussian

KW - Interpolation

KW - Nonstationary subdivision

KW - Radial basis function

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JO - SIAM Journal on Mathematical Analysis

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ER -

Analysis of univariate nonstationary subdivision schemes with application to gaussian-based interpolatory schemes

Abstract

Keywords

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