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Paper Abstract

Spectral radius of sets of matrices is a fundamental concept in studying the regularity of compactly supported wavelets. Here we review the basic properties of spectral radius and describe how to increase the efficiency of estimation of a lower bound for it. Spectral radius of sets of matrices can be defined by generalizing appropriate definitions of spectral radius of a single matrix. One definition, referred to as generalized spectral radius, is constructed as follows. Let (Sigma) be a collection of m square matrices of same size. Suppose L

_{n}((Sigma) ) is the set of products of length n of elements (Sigma) . Define p_{n}((Sigma) ) equals max_{A(epsilon}L_{n}[p(A)]^{1/n}where p(A) is the usual spectral radius of a matrix. Then the generalized spectral radius of (Sigma) is p((Sigma) ) equals lim sup_{nyields(infinity})p_{n}((Sigma) ). The standard method for estimating p((Sigma) ), through p_{n}((Sigma) ), involves m^{n}matrix calculations, one per each element of L_{n}((Sigma) ). We will describe a method which reduces this cost to m^{n}/n or less.
Paper Details

Date Published: 11 October 1994

PDF: 9 pages

Proc. SPIE 2303, Wavelet Applications in Signal and Image Processing II, (11 October 1994); doi: 10.1117/12.188808

Published in SPIE Proceedings Vol. 2303:

Wavelet Applications in Signal and Image Processing II

Andrew F. Laine; Michael A. Unser, Editor(s)

PDF: 9 pages

Proc. SPIE 2303, Wavelet Applications in Signal and Image Processing II, (11 October 1994); doi: 10.1117/12.188808

Show Author Affiliations

Mohsen Maesumi, Lamar Univ. (United States)

Published in SPIE Proceedings Vol. 2303:

Wavelet Applications in Signal and Image Processing II

Andrew F. Laine; Michael A. Unser, Editor(s)

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