Spectral Perturbation Optimization Of Matrix Pencils
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Spectral Perturbation Optimization Of Matrix Pencils
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Author : Hannes Gernandt
language : en
Publisher: BoD – Books on Demand
Release Date : 2021-01-01
Spectral Perturbation Optimization Of Matrix Pencils written by Hannes Gernandt and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-01 with Mathematics categories.
In this thesis we study the eigenvalues of linear matrix pencils and their behavior under perturbations of the pencil coefficients. In particular we address (i) Possibility of eigenvalue assignment under structured rank-one perturbations; (ii) Distance to nearest pencils with a prescribed set of eigenvalues in norm and gap distance; (iii) Computing nearest matrix pencils with prescribed eigenvalues using structured perturbations. In (i) and (ii) we exploit the connection between matrix pencils and certain subspaces via their Weyr characteristics. This provides a way of lifting perturbation measures for subspaces such as the gap distance to the set of matrix pencils. In (iii) one has to solve a large scale non-convex optimization problem which appears e.g. in optimal redesign of integrated circuits. We show how feasible solutions close to the optimal value can be computed. Finally, this is used to improve the bandwidth of two circuits (two-stage CMOS & μA741).
Matrix Pencils
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Author : B. Kagström
language : en
Publisher: Springer
Release Date : 2006-11-15
Matrix Pencils written by B. Kagström and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
On Linear Quadratic Optimal Control And Robustness Of Differential Algebraic Systems
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Author : Matthias Voigt
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2015-09-30
On Linear Quadratic Optimal Control And Robustness Of Differential Algebraic Systems written by Matthias Voigt and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-30 with Mathematics categories.
This thesis considers the linear-quadratic optimal control problem for differential-algebraic systems. In this first part, a complete theoretical analysis of this problem is presented. The basis is a new differential-algebraic version of the Kalman-Yakubovich-Popov (KYP) lemma. One focus is the analysis of the solution structure of the associated descriptor KYP inequality. In particular, rank-minimizing, stabilizing, and extremal solutions are characterized which gives a deep insight into the structure of the problem. Further contributions include new relations of the descriptor KYP inequality to structured matrix pencils, conditions for the existence of nonpositive solutions, and the application of the new theory to the characterization of dissipative systems and the factorization of rational matrix-valued functions. The second part of this thesis focuses on robustness questions, i.e., the influence of perturbations on system properties like dissipativity and stability is discussed. Characterizations for the distance of a dissipative systems to the set of non-dissipative systems are given which lead to a numerical method for computing this distance. Furthermore, the problem of computing the H-infinity-norm of a large-scale differential-algebraic system is considered. Two approaches for this computation are introduced and compared to each other.
Control And Optimization With Differential Algebraic Constraints
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Author : Lorenz T. Biegler
language : en
Publisher: SIAM
Release Date : 2012-01-01
Control And Optimization With Differential Algebraic Constraints written by Lorenz T. Biegler and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-01 with Control theory categories.
Differential-algebraic equations are the most natural way to mathematically model many complex systems in science and engineering. Once the model is derived, it is important to optimize the design parameters and control it in the most robust and efficient way to maximize performance. This book presents the latest theory and numerical methods for the optimal control of differential-algebraic equations. The following features are presented in a readable fashion so the results are accessible to the widest audience: the most recent theory, written by leading experts from a number of academic and nonacademic areas and departments; several state-of-the-art numerical methods; and real-world applications.
Perturbation Theory For Rectangular Matrix Pencils
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Author : Gilbert W. Stewart
language : en
Publisher:
Release Date : 1991
Perturbation Theory For Rectangular Matrix Pencils written by Gilbert W. Stewart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Matrices categories.
Abstract: "The theory of eigenvalues and eigenvectors of rectangular matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them [sic] disappear. However, there are applications in which the properties of the pencil ensure the existence of eigenvalues and eigenvectors. In this paper it is shown how to develop a perturbation theory for such pencils."
Low Rank Perturbation Of Regular Matrix Pencils With Symmetry Stuctures
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Author : Fernando de Terán
language : en
Publisher:
Release Date : 2019
Low Rank Perturbation Of Regular Matrix Pencils With Symmetry Stuctures written by Fernando de Terán and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Matrix Measure And Matrix Pencil Methods For Distributed Parameter System Stability Analysis And Stabilization
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Author : Mianmian Wang
language : en
Publisher:
Release Date : 1994
Matrix Measure And Matrix Pencil Methods For Distributed Parameter System Stability Analysis And Stabilization written by Mianmian Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Trust Region Methods
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Author : A. R. Conn
language : en
Publisher: SIAM
Release Date : 2000-01-01
Trust Region Methods written by A. R. Conn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
This is the first comprehensive reference on trust-region methods, a class of numerical algorithms for the solution of nonlinear convex optimization methods. Its unified treatment covers both unconstrained and constrained problems and reviews a large part of the specialized literature on the subject. It also provides an up-to-date view of numerical optimization.
Spectral Theory Of Operator Pencils Hermite Biehler Functions And Their Applications
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Author : Manfred Möller
language : en
Publisher: Birkhäuser
Release Date : 2015-06-11
Spectral Theory Of Operator Pencils Hermite Biehler Functions And Their Applications written by Manfred Möller and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-11 with Mathematics categories.
The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra. The second part is devoted to applications. Standard spectral problems in Hilbert spaces are of the form A-λI for an operator A, and self-adjoint operators are of particular interest and importance, both theoretically and in terms of applications. A characteristic feature of self-adjoint operators is that their spectra are real, and many spectral problems in theoretical physics and engineering can be described by using them. However, a large class of problems, in particular vibration problems with boundary conditions depending on the spectral parameter, are represented by operator polynomials that are quadratic in the eigenvalue parameter and whose coefficients are self-adjoint operators. The spectra of such operator polynomials are in general no more real, but still exhibit certain patterns. The distribution of these spectra is the main focus of the present volume. For some classes of quadratic operator polynomials, inverse problems are also considered. The connection between the spectra of such quadratic operator polynomials and generalized Hermite-Biehler functions is discussed in detail. Many applications are thoroughly investigated, such as the Regge problem and damped vibrations of smooth strings, Stieltjes strings, beams, star graphs of strings and quantum graphs. Some chapters summarize advanced background material, which is supplemented with detailed proofs. With regard to the reader’s background knowledge, only the basic properties of operators in Hilbert spaces and well-known results from complex analysis are assumed.