Construction of smooth refinable function vectors by cascade algorithms

Di Rong Chen

doi:10.1137/S0036142901392614

Construction of smooth refinable function vectors by cascade algorithms

Di Rong Chen^*

^*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 paper establishes an equivalent relation between the convergence of a cascade algorithm in Sobolev space and the convergence of an associated cascade algorithm in L_p space. It reduces the convergence in Sobolev space to that in L_p space. On the other hand, by the equivalence we present an algorithm for construction of refinement masks which generate convergent cascade algorithms in Sobolev space. It is very easy to implement the algorithm. Examples are given to illustrate the theory.

Original language	English
Pages (from-to)	1354-1368
Number of pages	15
Journal	SIAM Journal on Numerical Analysis
Volume	40
Issue number	4
DOIs	https://doi.org/10.1137/S0036142901392614
State	Published - Sep 2002

Keywords

Cascade algorithm
Factorization of mask
Joint spectral radius
Refinable function vector
Sobolev space

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10.1137/S0036142901392614

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abstract = "This paper establishes an equivalent relation between the convergence of a cascade algorithm in Sobolev space and the convergence of an associated cascade algorithm in Lp space. It reduces the convergence in Sobolev space to that in Lp space. On the other hand, by the equivalence we present an algorithm for construction of refinement masks which generate convergent cascade algorithms in Sobolev space. It is very easy to implement the algorithm. Examples are given to illustrate the theory.",

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AU - Chen, Di Rong

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N2 - This paper establishes an equivalent relation between the convergence of a cascade algorithm in Sobolev space and the convergence of an associated cascade algorithm in Lp space. It reduces the convergence in Sobolev space to that in Lp space. On the other hand, by the equivalence we present an algorithm for construction of refinement masks which generate convergent cascade algorithms in Sobolev space. It is very easy to implement the algorithm. Examples are given to illustrate the theory.

AB - This paper establishes an equivalent relation between the convergence of a cascade algorithm in Sobolev space and the convergence of an associated cascade algorithm in Lp space. It reduces the convergence in Sobolev space to that in Lp space. On the other hand, by the equivalence we present an algorithm for construction of refinement masks which generate convergent cascade algorithms in Sobolev space. It is very easy to implement the algorithm. Examples are given to illustrate the theory.

KW - Cascade algorithm

KW - Factorization of mask

KW - Joint spectral radius

KW - Refinable function vector

KW - Sobolev space

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VL - 40

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EP - 1368

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 4

ER -

Construction of smooth refinable function vectors by cascade algorithms

Abstract

Keywords

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