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Estimation of the Joint Spectral Radius

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Man–Machine Interactions 4

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 391))

Abstract

The joint spectral radius of a set of matrices is a generalization of the concept of spectral radius of a matrix. Such notation has many applications in the computer science, and more generally in applied mathematics. It has been used, for example in graph theory, control theory, capacity of codes, continuity of wavelets, overlap-free words, trackable graphs. It is impossible to provide analytic formulae for this quantity and therefore any estimation are highly desired. The main result of this paper is to provide an estimation of the joint spectral radius in the terms of matrices norms and spectral radii.

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Acknowledgments

The research presented here were done by the authors as parts of the projects funded by the National Science Centre granted according to decisions DEC-2012/07/B/ST7/01404, DEC-2012/05/B/ST7/00065 and DEC-2012/07/N/ST7/03236, respectively. The calculations were performed with the use of IT infrastructure of GeCONiI Upper Silesian Centre for Computational Science and Engineering (NCBiR grant no POIG.02.03.01-24-099/13).

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Authors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology, Gliwice, Poland

    Adam Czornik, Piotr Jurgaś & Michał Niezabitowski

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  1. Adam Czornik
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  2. Piotr Jurgaś
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  3. Michał Niezabitowski
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Correspondence to Adam Czornik .

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Editors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Aleksandra Gruca

  2. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Agnieszka Brachman

  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Stanisław Kozielski

  4. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Tadeusz Czachórski

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Czornik, A., Jurgaś, P., Niezabitowski, M. (2016). Estimation of the Joint Spectral Radius. In: Gruca, A., Brachman, A., Kozielski, S., Czachórski, T. (eds) Man–Machine Interactions 4. Advances in Intelligent Systems and Computing, vol 391. Springer, Cham. https://doi.org/10.1007/978-3-319-23437-3_34

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  • DOI: https://doi.org/10.1007/978-3-319-23437-3_34

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  • Online ISBN: 978-3-319-23437-3

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