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You searched for subject:(Joint spectral radius). Showing records 1 – 3 of 3 total matches.

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Université Catholique de Louvain

1. Theys, Jacques. Joint spectral radius : theory and approximations.

Degree: 2005, Université Catholique de Louvain

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. This 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. Although 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. In 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.

(FSA 3) – UCL, 2005

Advisors/Committee Members: UCL - FSA/INMA - Département d'ingénierie mathématique, Legat, Jean-Didier, Wirth, Fabian, Berthé, Valérie, Sepulchre, Rodolphe, Nesterov, Yurii, Van Dooren, Paul, Blondel, Vincent.

Subjects/Keywords: Joint spectral radius; Stability; Switched systems

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APA (6th Edition):

Theys, J. (2005). Joint spectral radius : theory and approximations. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/5161

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Theys, Jacques. “Joint spectral radius : theory and approximations.” 2005. Thesis, Université Catholique de Louvain. Accessed July 23, 2019. http://hdl.handle.net/2078.1/5161.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Theys, Jacques. “Joint spectral radius : theory and approximations.” 2005. Web. 23 Jul 2019.

Vancouver:

Theys J. Joint spectral radius : theory and approximations. [Internet] [Thesis]. Université Catholique de Louvain; 2005. [cited 2019 Jul 23]. Available from: http://hdl.handle.net/2078.1/5161.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Theys J. Joint spectral radius : theory and approximations. [Thesis]. Université Catholique de Louvain; 2005. Available from: http://hdl.handle.net/2078.1/5161

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


Université Catholique de Louvain

2. Chang, Chia-Tche. Heuristic optimization methods for three matrix problems.

Degree: 2012, Université Catholique de Louvain

Optimization is a major field in applied mathematics. Many applications involve the search of the best solution to a problem according to some criterion. Depending on the considered optimization problem, finding the best solution is not always possible in a reasonable amount of time. Heuristic algorithms are often used when the problem is too difficult to solve exactly. These methods are used to speed up the search for a good solution but they do not guarantee that an optimal solution will be found. In this thesis, we explore such heuristic approaches for three different matrix problems. First, we study the minimum-volume bounding box problem, which consists in finding the smallest rectangular parallelepiped enclosing a given set of points in the three-dimensional space. This problem appears for example in collision detection, which is a very important issue in computational geometry and computer graphics. In these applications, a solution has to be determined in a very short amount of time. We propose a new hybrid algorithm able to approximate optimal bounding boxes at a low computational cost. In particular, it is several orders of magnitude faster than the only currently known exact algorithm. Second, we investigate the subset selection problem. Given a large set of features, we want to choose a small subset containing the most relevant features while removing the redundant ones. This problem has applications in data mining since this can be seen as a dimensionality reduction problem. We develop several windowed algorithms that tackle the subset selection problem for the maximum-volume criterion, which is NP-hard. Finally, we address the topic of the approximation of the joint spectral radius. This quantity characterizes the growth rate of product of matrices and is NP-hard to approximate. The joint spectral radius appears in many fields, including system theory, graph theory, combinatorics, language theory... We present an experimental study of existing approaches and propose a new genetic-based algorithm that is able to find bounds on the joint spectral radius in a short amount of time.

(FSA 3)  – UCL, 2012

Advisors/Committee Members: UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique, Blondel, Vincent, Van Dooren, Paul, Glineur, François, Jungers, Raphaël, Diehl, Moritz, Ipsen, Ilse.

Subjects/Keywords: Heuristics; Metaheuristics; Feature selection; Dynamical system; Switching system; Genetic algorithm; Optimization; Algorithmics; Oriented bounding box; Subset selection; Joint spectral radius; Computational methods; Experimental analysis; Computational geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Chang, C. (2012). Heuristic optimization methods for three matrix problems. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/120115

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Chang, Chia-Tche. “Heuristic optimization methods for three matrix problems.” 2012. Thesis, Université Catholique de Louvain. Accessed July 23, 2019. http://hdl.handle.net/2078.1/120115.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Chang, Chia-Tche. “Heuristic optimization methods for three matrix problems.” 2012. Web. 23 Jul 2019.

Vancouver:

Chang C. Heuristic optimization methods for three matrix problems. [Internet] [Thesis]. Université Catholique de Louvain; 2012. [cited 2019 Jul 23]. Available from: http://hdl.handle.net/2078.1/120115.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chang C. Heuristic optimization methods for three matrix problems. [Thesis]. Université Catholique de Louvain; 2012. Available from: http://hdl.handle.net/2078.1/120115

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Sert, Cagri. Joint Spectrum and Large Deviation Principles for Random Products of Matrices : Spectre joint et principes de grandes déviations pour les produits aléatoires des matrices.

Degree: Docteur es, Mathématiques fondamentales, 2016, Paris Saclay

Après une introduction générale et la présentation d'un exemple explicite dans le chapitre 1, nous exposons certains outils et techniques généraux dans le chapitre 2.- dans le chapitre 3, nous démontrons l'existence d'un principe de grandes déviations (PGD) pour les composantes de Cartan le long des marches aléatoires sur les groupes linéaires semi -simples G. L'hypothèse principale porte sur le support S de la mesure de la probabilité en question et demande que S engendre un semi-groupe Zariski dense. - Dans le chapitre 4, nous introduisons un objet limite (une partie de la chambre de Weyl) que l'on associe à une partie bornée S de G et que nous appelons le spectre joint J(S) de S. Nous étudions ses propriétés et démontrons que J(S) est une partie convexe compacte d'intérieur non-vide dès que S engendre un semi -groupe Zariski dense. Nous relions le spectre joint avec la notion classique du rayon spectral joint et la fonction de taux du PGD pour les marches aléatoires. - Dans le chapitre 5, nous introduisons une fonction de comptage exponentiel pour un S fini dans G, nous étudions ses propriétés que nous relions avec J(S) et démontrons un théorème de croissance exponentielle dense. - Dans le chapitre 6, nous démontrons le PGD pour les composantes d'Iwasawa le long des marches aléatoires sur G. L'hypothèse principale demande l'absolue continuité de la mesure de probabilité par rapport à la mesure de Haar.- Dans le chapitre 7, nous développons des outils pour aborder une question de Breuillard sur la rigidité du rayon spectral d'une marche aléatoire sur le groupe libre. Nous y démontrons un résultat de rigidité géométrique.

After giving a detailed introduction andthe presentation of an explicit example to illustrateour study in Chapter 1, we exhibit some general toolsand techniques in Chapter 2. Subsequently,- In Chapter 3, we prove the existence of a large deviationprinciple (LDP) with a convex rate function, forthe Cartan components of the random walks on linearsemisimple groups G. The main hypothesis is onthe support S of the probability measure in question,and asks S to generate a Zariski dense semigroup.- In Chapter 4, we introduce a limit object (a subsetof the Weyl chamber) that we associate to a boundedsubset S of G. We call this the joint spectrum J(S)of S. We study its properties and show that for asubset S generating a Zariski dense semigroup, J(S)is convex body, i.e. a convex compact subset of nonemptyinterior. We relate the joint spectrum withthe classical notion of joint spectral radius and therate function of LDP for random walks on G.- In Chapter 5, we introduce an exponential countingfunction for a nite S in G. We study its properties,relate it to joint spectrum of S and prove a denseexponential growth theorem.- In Chapter 6, we prove the existence of an LDPfor Iwasawa components of random walks on G. Thehypothesis asks for a condition of absolute continuityof the probability measure with respect to the Haarmeasure.- In Chapter 7, we develop some tools to tackle aquestion of Breuillard on the…

Advisors/Committee Members: Breuillard, Emmanuel (thesis director).

Subjects/Keywords: Produits aléatoires des matrices; Principes de grandes déviations; Groupes linéaires; Rayon spectral joint; Croissance des groupes; Groupe libre; Croissance des groupes; Random matrix products; Large deviation principle; Linear groups; Joint spectral radius; Growth of groups; Free group; Growth of groups

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Sert, C. (2016). Joint Spectrum and Large Deviation Principles for Random Products of Matrices : Spectre joint et principes de grandes déviations pour les produits aléatoires des matrices. (Doctoral Dissertation). Paris Saclay. Retrieved from http://www.theses.fr/2016SACLS500

Chicago Manual of Style (16th Edition):

Sert, Cagri. “Joint Spectrum and Large Deviation Principles for Random Products of Matrices : Spectre joint et principes de grandes déviations pour les produits aléatoires des matrices.” 2016. Doctoral Dissertation, Paris Saclay. Accessed July 23, 2019. http://www.theses.fr/2016SACLS500.

MLA Handbook (7th Edition):

Sert, Cagri. “Joint Spectrum and Large Deviation Principles for Random Products of Matrices : Spectre joint et principes de grandes déviations pour les produits aléatoires des matrices.” 2016. Web. 23 Jul 2019.

Vancouver:

Sert C. Joint Spectrum and Large Deviation Principles for Random Products of Matrices : Spectre joint et principes de grandes déviations pour les produits aléatoires des matrices. [Internet] [Doctoral dissertation]. Paris Saclay; 2016. [cited 2019 Jul 23]. Available from: http://www.theses.fr/2016SACLS500.

Council of Science Editors:

Sert C. Joint Spectrum and Large Deviation Principles for Random Products of Matrices : Spectre joint et principes de grandes déviations pour les produits aléatoires des matrices. [Doctoral Dissertation]. Paris Saclay; 2016. Available from: http://www.theses.fr/2016SACLS500

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