The Joint Spectral Radius : Theory and Applications / by Raphaël Jungers.

Springer eBooks

I Theory -- Basics -- Classical Results and Problems -- Nonnegative Integer Matrices -- On the Finiteness Property for Rational Matrices -- II Applications -- Continuity of Wavelet Functions -- Capacity of Codes -- Overlap-Free Words -- Trackable Graphs -- Conclusion -- III Appendices -- Appendix A Numerical Values for Overlap-Free Words.

The first part of this monograph is dedicated to theoretical results. The first two chapters present the above mentioned survey on the joint spectral radius. Its minimum growth counterpart, the joint spectral subradius, is also considered. The next two chapters point out two specific theoretical topics, that are important in practical applications: the particular case of nonnegative matrices, and the Finiteness Property. The second part considers applications involving the joint spectral radius. The author first presents the continuity of wavelet. He then studies the problem of the capacity of codes submitted to forbidden difference constraints. The notion of overlap-free words is then discussed, a problem that arises in combinatorics on words. The book then ends with the problem of trackability of sensor networks, and shows how the theoretical results developed in the first part allow to solve this problem efficiently.

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