Estimation of the joint spectral radius

Adam Czornik; Piotr Jurgás; Michał Niezabitowski

doi:10.1007/978-3-319-23437-3_34

Estimation of the joint spectral radius

Department of Automatic Control and Robotics (RAU/RAU3)

Silesian University of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Citations (Scopus)

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.

Original language	English
Title of host publication	Man–Machine Interactions - 4th International Conference on Man–Machine Interactions, ICMMI 2015
Editors	Tadeusz Czachórski, Aleksandra Gruca, Agnieszka Brachman, Stanisław Kozielski, Tadeusz Czachórski
Publisher	Springer Verlag
Pages	401-410
Number of pages	10
ISBN (Print)	9783319234366
DOIs	https://doi.org/10.1007/978-3-319-23437-3_34
Publication status	Published - 2016
Event	4th International Conference on Man–Machine Interactions, ICMMI 2015 - Kocierz Pass, Poland Duration: 6 Oct 2015 → 9 Oct 2015

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	391
ISSN (Print)	2194-5357

Conference

Conference	4th International Conference on Man–Machine Interactions, ICMMI 2015
Country/Territory	Poland
City	Kocierz Pass
Period	6/10/15 → 9/10/15

Keywords

Capacity of codes
Continuity of wavelets
Estimation
Graph theory
Joint spectral radius
Overlap-free words
Trackable graphs

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science

Access to Document

10.1007/978-3-319-23437-3_34

Cite this

Czornik, A., Jurgás, P., & Niezabitowski, M. (2016). Estimation of the joint spectral radius. In T. Czachórski, A. Gruca, A. Brachman, S. Kozielski, & T. Czachórski (Eds.), Man–Machine Interactions - 4th International Conference on Man–Machine Interactions, ICMMI 2015 (pp. 401-410). (Advances in Intelligent Systems and Computing; Vol. 391). Springer Verlag. https://doi.org/10.1007/978-3-319-23437-3_34

Czornik, Adam ; Jurgás, Piotr ; Niezabitowski, Michał. / Estimation of the joint spectral radius. Man–Machine Interactions - 4th International Conference on Man–Machine Interactions, ICMMI 2015. editor / Tadeusz Czachórski ; Aleksandra Gruca ; Agnieszka Brachman ; Stanisław Kozielski ; Tadeusz Czachórski. Springer Verlag, 2016. pp. 401-410 (Advances in Intelligent Systems and Computing).

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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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author = "Adam Czornik and Piotr Jurg{\'a}s and Micha{\l} Niezabitowski",

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Czornik, A, Jurgás, P & Niezabitowski, M 2016, Estimation of the joint spectral radius. in T Czachórski, A Gruca, A Brachman, S Kozielski & T Czachórski (eds), Man–Machine Interactions - 4th International Conference on Man–Machine Interactions, ICMMI 2015. Advances in Intelligent Systems and Computing, vol. 391, Springer Verlag, pp. 401-410, 4th International Conference on Man–Machine Interactions, ICMMI 2015, Kocierz Pass, Poland, 6/10/15. https://doi.org/10.1007/978-3-319-23437-3_34

Estimation of the joint spectral radius. / Czornik, Adam; Jurgás, Piotr; Niezabitowski, Michał.
Man–Machine Interactions - 4th International Conference on Man–Machine Interactions, ICMMI 2015. ed. / Tadeusz Czachórski; Aleksandra Gruca; Agnieszka Brachman; Stanisław Kozielski; Tadeusz Czachórski. Springer Verlag, 2016. p. 401-410 (Advances in Intelligent Systems and Computing; Vol. 391).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Jurgás, Piotr

AU - Niezabitowski, Michał

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Capacity of codes

KW - Continuity of wavelets

KW - Estimation

KW - Graph theory

KW - Joint spectral radius

KW - Overlap-free words

KW - Trackable graphs

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Czornik A, Jurgás P, Niezabitowski M. Estimation of the joint spectral radius. In Czachórski T, Gruca A, Brachman A, Kozielski S, Czachórski T, editors, Man–Machine Interactions - 4th International Conference on Man–Machine Interactions, ICMMI 2015. Springer Verlag. 2016. p. 401-410. (Advances in Intelligent Systems and Computing). doi: 10.1007/978-3-319-23437-3_34

Estimation of the joint spectral radius

Abstract

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Keywords

ASJC Scopus subject areas

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