Stability implies convergence of cascade algorithms in Solobev space

Di Rong Chen; Xiaobo Zheng

doi:10.1006/jmaa.2001.7782

Stability implies convergence of cascade algorithms in Solobev space

Di Rong Chen^*
, Xiaobo Zheng

^*Corresponding author for this work

School of Mathematical Sciences

Hubei University for Nationalities

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

9 Scopus citations

Abstract

This article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in Sobolev space to which the refinable function vector belongs. An example of Hermite interpolants is presented to illustrate the result.

Original language	English
Pages (from-to)	41-52
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	268
Issue number	1
DOIs	https://doi.org/10.1006/jmaa.2001.7782
State	Published - 1 Apr 2002

Keywords

Cascade algorithm
Hermite interpolant
Sobolev space
Stability

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title = "Stability implies convergence of cascade algorithms in Solobev space",

abstract = "This article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in Sobolev space to which the refinable function vector belongs. An example of Hermite interpolants is presented to illustrate the result.",

keywords = "Cascade algorithm, Hermite interpolant, Sobolev space, Stability",

author = "Chen, \{Di Rong\} and Xiaobo Zheng",

year = "2002",

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doi = "10.1006/jmaa.2001.7782",

language = "英语",

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T1 - Stability implies convergence of cascade algorithms in Solobev space

AU - Chen, Di Rong

AU - Zheng, Xiaobo

PY - 2002/4/1

Y1 - 2002/4/1

N2 - This article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in Sobolev space to which the refinable function vector belongs. An example of Hermite interpolants is presented to illustrate the result.

AB - This article proves that the stability of the shifts of a refinable function vector ensures the convergence of the corresponding cascade algorithm in Sobolev space to which the refinable function vector belongs. An example of Hermite interpolants is presented to illustrate the result.

KW - Cascade algorithm

KW - Hermite interpolant

KW - Sobolev space

KW - Stability

UR - https://www.scopus.com/pages/publications/0036537564

U2 - 10.1006/jmaa.2001.7782

DO - 10.1006/jmaa.2001.7782

M3 - 文章

AN - SCOPUS:0036537564

SN - 0022-247X

VL - 268

SP - 41

EP - 52

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Stability implies convergence of cascade algorithms in Solobev space

Abstract

Keywords

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