Computing the joint spectral radius

被引：91
作者：
Gripenberg, G
机构：
[1] University of Helsinki, Department of Mathematics, 00014 Helsinki
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 1996年 / 234卷
关键词：
D O I：
10.1016/0024-3795(94)00082-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents algorithms for finding an arbiarily small interval that contains the joint spectral radius of a finite set of matrices. It also presents a numerical criterion for verifying in certain cases that the joint spectral radius is the maximum of the spectral radii of the given matrices. Error bounds are derived for the case where calculations are done with finite precision and the matrices are not known exactly. The algorithms are implemented and applied to estimate Holder exponents of the orthonormal wavelets (N) phi constructed by Daubechies for 3 less than or equal to N less than or equal to 8.
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页码：43 / 60
页数：18
相关论文
共 8 条
[1]   BOUNDED SEMIGROUPS OF MATRICES [J].
BERGER, MA ;
WANG, Y .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 166 :21-27
[2]   THE CHARACTERIZATION OF CONTINUOUS, 4-COEFFICIENT SCALING FUNCTIONS AND WAVELETS [J].
COLELLA, D ;
HEIL, C .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1992, 38 (02) :876-881
[3]   SETS OF MATRICES ALL INFINITE PRODUCTS OF WHICH CONVERGE [J].
DAUBECHIES, I ;
LAGARIAS, JC .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 161 :227-263
[4]   2-SCALE DIFFERENCE-EQUATIONS .2. LOCAL REGULARITY, INFINITE PRODUCTS OF MATRICES AND FRACTALS [J].
DAUBECHIES, I ;
LAGARIAS, JC .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (04) :1031-1079
[5]   ORTHONORMAL BASES OF COMPACTLY SUPPORTED WAVELETS [J].
DAUBECHIES, I .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (07) :909-996
[6]  
HEIL C, IN PRESS WAVELETS MA
[7]   THE FINITENESS CONJECTURE FOR THE GENERALIZED SPECTRAL-RADIUS OF A SET OF MATRICES [J].
LAGARIAS, JC ;
WANG, Y .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 214 :17-42
[8]  
Wilkinson J. H., 1965, The Algebraic Eigenvalue Problem
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