Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks

Di Rong Chen; Gerlind Plonka

doi:10.1006/jath.2002.3682

Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks

Di Rong Chen
, Gerlind Plonka^*

^*Corresponding author for this work

School of Mathematical Sciences

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

9 Scopus citations

Abstract

In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm, corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks.

Original language	English
Pages (from-to)	133-155
Number of pages	23
Journal	Journal of Approximation Theory
Volume	119
Issue number	2
DOIs	https://doi.org/10.1006/jath.2002.3682
State	Published - 1 Dec 2002

Keywords

Cascade algorithm
Joint spectral radius
Perturbation of refinable functions
Sobolev space

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10.1006/jath.2002.3682

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title = "Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks",

abstract = "In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm, corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks.",

keywords = "Cascade algorithm, Joint spectral radius, Perturbation of refinable functions, Sobolev space",

author = "Chen, \{Di Rong\} and Gerlind Plonka",

year = "2002",

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doi = "10.1006/jath.2002.3682",

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T1 - Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks

AU - Chen, Di Rong

AU - Plonka, Gerlind

PY - 2002/12/1

Y1 - 2002/12/1

N2 - In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm, corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks.

AB - In this paper, the convergence of the cascade algorithm in a Sobolev space is considered if the refinement mask is perturbed. It is proved that the cascade algorithm, corresponding to a slightly perturbed mask converges. Moreover, the perturbation of the resulting limit function is estimated in terms of that of the masks.

KW - Cascade algorithm

KW - Joint spectral radius

KW - Perturbation of refinable functions

KW - Sobolev space

UR - https://www.scopus.com/pages/publications/0036899407

U2 - 10.1006/jath.2002.3682

DO - 10.1006/jath.2002.3682

M3 - 文章

AN - SCOPUS:0036899407

SN - 0021-9045

VL - 119

SP - 133

EP - 155

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 2

ER -

Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks

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Keywords

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