Spectral Perturbation Optimization Of Matrix Pencils

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Spectral Perturbation & Optimization of Matrix Pencils

Author : Hannes Gernandt
Publisher : BoD – Books on Demand
ISBN 13 : 3863602463
Total Pages : 134 pages
Book Rating : 4.8/5 (636 download)

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Book Synopsis Spectral Perturbation & Optimization of Matrix Pencils by : Hannes Gernandt

Download or read book Spectral Perturbation & Optimization of Matrix Pencils written by Hannes Gernandt and published by BoD – Books on Demand. This book was released on 2021-01-01 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : B. Kagström
Publisher : Springer
ISBN 13 : 3540394478
Total Pages : 304 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Matrix Pencils by : B. Kagström

Download or read book Matrix Pencils written by B. Kagström and published by Springer. This book was released on 2006-11-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On Linear-Quadratic Optimal Control and Robustness of Differential-Algebraic Systems

Author : Matthias Voigt
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832541187
Total Pages : 314 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis On Linear-Quadratic Optimal Control and Robustness of Differential-Algebraic Systems by : Matthias Voigt

Download or read book On Linear-Quadratic Optimal Control and Robustness of Differential-Algebraic Systems written by Matthias Voigt and published by Logos Verlag Berlin GmbH. This book was released on 2015-09-30 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Lorenz T. Biegler
Publisher : SIAM
ISBN 13 : 9781611972252
Total Pages : 355 pages
Book Rating : 4.9/5 (722 download)

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Book Synopsis Control and Optimization with Differential-Algebraic Constraints by : Lorenz T. Biegler

Download or read book Control and Optimization with Differential-Algebraic Constraints written by Lorenz T. Biegler and published by SIAM. This book was released on 2012-01-01 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Panorama of Mathematics: Pure and Applied

Author : Carlos M. da Fonseca
Publisher : American Mathematical Soc.
ISBN 13 : 1470416689
Total Pages : 292 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Panorama of Mathematics: Pure and Applied by : Carlos M. da Fonseca

Download or read book A Panorama of Mathematics: Pure and Applied written by Carlos M. da Fonseca and published by American Mathematical Soc.. This book was released on 2016-02-26 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Mathematics and its Applications-2014, held from November 14-17, 2014, at Kuwait University, Safat, Kuwait. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. Papers contained in this volume cover various topics in pure and applied mathematics ranging from an introductory study of quotients and homomorphisms of C-systems, also known as contextual pre-categories, to the most important consequences of the so-called Fokas method. Also covered are multidisciplinary topics such as new structural and spectral matricial results, acousto-electromagnetic tomography method, a recent hybrid imaging technique, some numerical aspects of sonic-boom minimization, PDE eigenvalue problems, von Neumann entropy in graph theory, the relative entropy method for hyperbolic systems, conductances on grids, inverse problems in magnetohydrodynamics, location and size estimation of small rigid bodies using elastic far-fields, and the space-time fractional Schrödinger equation, just to cite a few. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpufThis volume contains the proceedings of the Conference on Mathematics and its Applications–2014, held from November 14–17, 2014, at Kuwait University, Safat, Kuwait. - See more at: http://s350148651-preview.tizrapublisher.com/conm-658/#sthash.74nRhV3y.dpuf

Perturbation Theory for Rectangular Matrix Pencils

Author : Gilbert W. Stewart
Publisher :
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4.:/5 (269 download)

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Book Synopsis Perturbation Theory for Rectangular Matrix Pencils by : Gilbert W. Stewart

Download or read book Perturbation Theory for Rectangular Matrix Pencils written by Gilbert W. Stewart and published by . This book was released on 1991 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1770 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Trust Region Methods

Author : A. R. Conn
Publisher : SIAM
ISBN 13 : 0898719852
Total Pages : 978 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Trust Region Methods by : A. R. Conn

Download or read book Trust Region Methods written by A. R. Conn and published by SIAM. This book was released on 2000-01-01 with total page 978 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Manfred Möller
Publisher : Birkhäuser
ISBN 13 : 3319170708
Total Pages : 418 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications by : Manfred Möller

Download or read book Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications written by Manfred Möller and published by Birkhäuser. This book was released on 2015-06-11 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stability and Stabilization of Time-Delay Systems

Author : Wim Michiels
Publisher : SIAM
ISBN 13 : 0898716322
Total Pages : 383 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Stability and Stabilization of Time-Delay Systems by : Wim Michiels

Download or read book Stability and Stabilization of Time-Delay Systems written by Wim Michiels and published by SIAM. This book was released on 2007-01-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overall solution to the (robust) stability analysis and stabilisation problem of linear time-delay systems.

Handbook of Linear Algebra

Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1498785603
Total Pages : 1906 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Handbook of Linear Algebra by : Leslie Hogben

Download or read book Handbook of Linear Algebra written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and

Nonconservative Stability Problems of Modern Physics

Author : Oleg N. Kirillov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110653869
Total Pages : 484 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Nonconservative Stability Problems of Modern Physics by : Oleg N. Kirillov

Download or read book Nonconservative Stability Problems of Modern Physics written by Oleg N. Kirillov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-03-08 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Low Rank Perturbation of Regular Matrix Pencils with Symmetry Stuctures

Author : Fernando de Terán
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Low Rank Perturbation of Regular Matrix Pencils with Symmetry Stuctures by : Fernando de Terán

Download or read book Low Rank Perturbation of Regular Matrix Pencils with Symmetry Stuctures written by Fernando de Terán and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Matrix Measure and Matrix Pencil Methods for Distributed Parameter System Stability Analysis and Stabilization

Author : Mianmian Wang
Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Matrix Measure and Matrix Pencil Methods for Distributed Parameter System Stability Analysis and Stabilization by : Mianmian Wang

Download or read book Matrix Measure and Matrix Pencil Methods for Distributed Parameter System Stability Analysis and Stabilization written by Mianmian Wang and published by . This book was released on 1994 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing

Author : Tetsuya Sakurai
Publisher : Springer
ISBN 13 : 3319624261
Total Pages : 312 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing by : Tetsuya Sakurai

Download or read book Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing written by Tetsuya Sakurai and published by Springer. This book was released on 2018-01-03 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Engineering Mathematics II

Author : Sergei Silvestrov
Publisher : Springer
ISBN 13 : 3319421050
Total Pages : 437 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Engineering Mathematics II by : Sergei Silvestrov

Download or read book Engineering Mathematics II written by Sergei Silvestrov and published by Springer. This book was released on 2017-02-10 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analytic Perturbation Theory and Its Applications

Author : Konstantin E. Avrachenkov
Publisher : SIAM
ISBN 13 : 1611973139
Total Pages : 384 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Analytic Perturbation Theory and Its Applications by : Konstantin E. Avrachenkov

Download or read book Analytic Perturbation Theory and Its Applications written by Konstantin E. Avrachenkov and published by SIAM. This book was released on 2013-12-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.