Fast And Precise Approximations Of The Joint Spectral Radius
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Fast And Precise Approximations Of The Joint Spectral Radius
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Author : Vincent Blondel
language : en
Publisher:
Release Date : 2007
Fast And Precise Approximations Of The Joint Spectral Radius written by Vincent Blondel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
In this paper, we introduce a procedure for approximating the joint spectral radius of a finite set of matrices with arbitrary precision. Our approximation procedure is based on semidefinite liftings and can be implemented in a recursive way. For two matrices even the first step of the procedure gives an approximation, whose relative quality is at least 1/√2, that is, more than 70%. The subsequent steps improve the quality but also increase the dimension of the auxiliary problem from which this approximation can be found. In an improved version of our approximation procedure we show how a relative quality of (1/√2(1/k)) can be obtained by evaluating the spectral radius of a single matrix of dimension nk nk+1)/2 where n is the dimension of the initial matrices. This result is computationally optimal in the sense that it provides an approximation of relative quality 1-[epsilon] in time polynomial in n(1/[epsilon]) and it is known that, unless P = NP, no such algorithm is possible that runs in time polynomial in n and 1/[epsilon]. For the special case of matrices with non-negative entries we prove that... where A(*k) denotes the kth Kroneckerp owerof A. An approximation of relative quality (1/2)(1/k) can therefore be obtained by computing the spectral radius of a single matrix of dimension n(k). From these inequalities it also follows that the spectral radius is given by the simple expression... where it is somewhat surprising to notice that the right hand side does not directly involve any mixed products between the matrices A1 and A2.
Fast And Precise Approximations Of The Joint Spectral Radius
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Author : Vincent D. Blondel
language : en
Publisher:
Release Date : 2003
Fast And Precise Approximations Of The Joint Spectral Radius written by Vincent D. Blondel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
The Joint Spectral Radius
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Author : Raphaël Jungers
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-19
The Joint Spectral Radius written by Raphaël Jungers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-19 with Technology & Engineering categories.
This monograph is based on the Ph.D. Thesis of the author [58]. Its goal is twofold: First, it presents most researchwork that has been done during his Ph.D., or at least the part of the work that is related with the joint spectral radius. This work was concerned with theoretical developments (part I) as well as the study of some applications (part II). As a second goal, it was the author’s feeling that a survey on the state of the art on the joint spectral radius was really missing in the literature, so that the ?rst two chapters of part I present such a survey. The other chapters mainly report personal research, except Chapter 5 which presents animportantapplicationofthejointspectralradius:thecontinuityofwavelet functions. The ?rst part of this monograph is dedicated to theoretical results. The ?rst 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 speci?c theoretical topics, that are important in practical applications: the particular case of nonne- tive matrices, and the Finiteness Property. The second part considers applications involving the joint spectral radius.
Combinatorics Automata And Number Theory
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Author : Valérie Berthé
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-12
Combinatorics Automata And Number Theory written by Valérie Berthé and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-12 with Mathematics categories.
This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and its Applications cover their subjects comprehensively. Less important results may be summarised as exercises at the ends of chapters, For technicalities, readers can be referred to the bibliography, which is expected to be comprehensive. As a result, volumes are encyclopedic references or manageable guides to major subjects.
Man Machine Interactions 4
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Author : Aleksandra Gruca
language : en
Publisher: Springer
Release Date : 2015-10-01
Man Machine Interactions 4 written by Aleksandra Gruca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-01 with Technology & Engineering categories.
This book provides an overview of the current state of research on development and application of methods, algorithms, tools and systems associated with the studies on man-machine interaction. Modern machines and computer systems are designed not only to process information, but also to work in dynamic environment, supporting or even replacing human activities in areas such as business, industry, medicine or military. The interdisciplinary field of research on man-machine interactions focuses on broad range of aspects related to the ways in which human make or use computational artifacts, systems and infrastructure. This monograph is the fourth edition in the series and presents new concepts concerning analysis, design and evaluation of man-machine systems. The selection of high-quality, original papers covers a wide scope of research topics focused on the main problems and challenges encountered within rapidly evolving new forms of human-machine relationships. The presented material is structured into following sections: human-computer interfaces, robot, control, embedded and navigation systems, bio-data analysis and mining, biomedical signal processing, image and motion data processing, decision support and expert systems, pattern recognition, fuzzy systems, algorithms and optimisation, computer networks and mobile technologies, and data management systems.
Siam Journal On Matrix Analysis And Applications
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Author :
language : en
Publisher:
Release Date : 2005
Siam Journal On Matrix Analysis And Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Aanwinsten Van De Centrale Bibliotheek Queteletfonds
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Author : Bibliothèque centrale (Fonds Quetelet)
language : en
Publisher:
Release Date : 2004
Aanwinsten Van De Centrale Bibliotheek Queteletfonds written by Bibliothèque centrale (Fonds Quetelet) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Wavelets And Multiwavelets
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Author : Fritz Keinert
language : en
Publisher: CRC Press
Release Date : 2003-11-12
Wavelets And Multiwavelets written by Fritz Keinert and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-12 with Mathematics categories.
Theoretically, multiwavelets hold significant advantages over standard wavelets, particularly for solving more complicated problems, and hence are of great interest. Meeting the needs of engineers and mathematicians, this book provides a comprehensive overview of multiwavelets. The author presents the theory of wavelets from the viewpoint of genera
The Dynamics Of Control
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Author : Fritz Colonius
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Dynamics Of Control written by Fritz Colonius and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This new text/reference is an excellent resource for the foundations and applications of control theory and nonlinear dynamics. All graduates, practitioners, and professionals in control theory, dynamical systems, perturbation theory, engineering, physics and nonlinear dynamics will find the book a rich source of ideas, methods and applications. With its careful use of examples and detailed development, it is suitable for use as a self-study/reference guide for all scientists and engineers.
Chebyshev And Fourier Spectral Methods
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Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2001-12-03
Chebyshev And Fourier Spectral Methods written by John P. Boyd and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-03 with Mathematics categories.
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.