Joint spectral radius : theory and approximations/
Year: 2005
Type: article
Abstract: The spectral radius of a matrix is a widely used concept in linear algebra. It expresses the asymptotic growth rate of successive powers of the matrix. This concept can be extended to sets of matrices, leading to the notion of "joint spectral radius". The joint spectral radius of a set of matrices was defined in the 1960's, but has only been used extensively since the 1990's.\nThis concept is useful to study the behavior of multi-agent systems, to determine the continuity of wavelet basis functions or for expressing the capacity of binary codes.\nAlthough the joint spectral radius shares some properties with the usual spectral radius, it is much harder to compute, and the problem of approximating it is NP-hard.\nIn this thesis, we first review theoretical results that lead to basic approximations of the joint spectral radius. Then, we list various specific cases where it is effectively computable, before presenting a specific type of sets of matrices, for which we solve the problem of computing it with a polynomial computational cost.
Author: Jacques Theys
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1631683393