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Author: Hannes Gernandt
Publisher: BoD – Books on Demand
ISBN: 3863602463
Category : Mathematics
Languages : en
Pages : 134
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Book Description
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).
Author: Hannes Gernandt
Publisher: BoD – Books on Demand
ISBN: 3863602463
Category : Mathematics
Languages : en
Pages : 134
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Book Description
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).
Author: Oleg N. Kirillov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110653869
Category : Science
Languages : en
Pages : 716
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Book Description
This updated revision gives a complete and topical overview on Nonconservative Stability which is essential for many areas of science and technology ranging from particles trapping in optical tweezers and dynamics of subcellular structures to dissipative and radiative instabilities in fluid mechanics, astrophysics and celestial mechanics. The author presents relevant mathematical concepts as well as rigorous stability results and numerous classical and contemporary examples from non-conservative mechanics and non-Hermitian physics. New coverage of ponderomotive magnetism, experimental detection of Ziegler’s destabilization phenomenon and theory of double-diffusive instabilities in magnetohydrodynamics.
Author: Matthias Voigt
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832541187
Category : Mathematics
Languages : en
Pages : 314
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Book Description
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.
Author: Tetsuya Sakurai
Publisher: Springer
ISBN: 3319624261
Category : Computers
Languages : en
Pages : 312
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Book Description
This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.
Author: Lorenz T. Biegler
Publisher: SIAM
ISBN: 9781611972252
Category : Control theory
Languages : en
Pages : 355
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Book Description
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.
Author: Sergei Silvestrov
Publisher: Springer
ISBN: 3319421050
Category : Computers
Languages : en
Pages : 437
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Book Description
This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The book consists of contributed chapters covering research developed as a result of a focused international seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications. It serves as a source of inspiration for a broad spectrum of researchers and research students in applied mathematics, as well as in the areas of applications of mathematics considered in the book.
Author: Konstantin E. Avrachenkov
Publisher: SIAM
ISBN: 1611973139
Category : Mathematics
Languages : en
Pages : 384
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Book Description
Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is important to know what happens when these values are changed. The study of single-parameter deviations provides a natural starting point for this analysis in many special settings in the sciences, engineering, and economics. The difference between the actual and nominal values of the perturbation parameter is small but unknown, and it is important to understand the asymptotic behavior of the system as the perturbation tends to zero. This is particularly true in applications with an apparent discontinuity in the limiting behavior?the so-called singularly perturbed problems. Analytic Perturbation Theory and Its Applications includes a comprehensive treatment of analytic perturbations of matrices, linear operators, and polynomial systems, particularly the singular perturbation of inverses and generalized inverses. It also offers original applications in Markov chains, Markov decision processes, optimization, and applications to Google PageRank? and the Hamiltonian cycle problem as well as input retrieval in linear control systems and a problem section in every chapter to aid in course preparation.
Author:
Publisher:
ISBN:
Category : Computer networks
Languages : en
Pages : 856
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Book Description
Author: Lloyd N. Trefethen
Publisher: Princeton University Press
ISBN: 0691213100
Category : Mathematics
Languages : en
Pages : 626
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Book Description
Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 960
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Book Description
