Share Email Print

Proceedings Paper

Spectral radius of sets of matrices
Author(s): Mohsen Maesumi
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

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 Ln((Sigma) ) is the set of products of length n of elements (Sigma) . Define pn((Sigma) ) equals maxA(epsilon Ln [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 supnyields(infinity )pn((Sigma) ). The standard method for estimating p((Sigma) ), through pn((Sigma) ), involves mn matrix calculations, one per each element of Ln((Sigma) ). We will describe a method which reduces this cost to mn/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
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)

© SPIE. Terms of Use
Back to Top