Symplectic Methods For The Symplectic Eigenproblem

Author : Heike Fassbender
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 51,9 Mb
Release : 2007-05-08
Category : Computers
ISBN : 9780306469787

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Symplectic Methods for the Symplectic Eigenproblem by Heike Fassbender Pdf

The solution of eigenvalue problems is an integral part of many scientific computations. For example, the numerical solution of problems in structural dynamics, electrical networks, macro-economics, quantum chemistry, and c- trol theory often requires solving eigenvalue problems. The coefficient matrix of the eigenvalue problem may be small to medium sized and dense, or large and sparse (containing many zeroelements). In the past tremendous advances have been achieved in the solution methods for symmetric eigenvalue pr- lems. The state of the art for nonsymmetric problems is not so advanced; nonsymmetric eigenvalue problems can be hopelessly difficult to solve in some situations due, for example, to poor conditioning. Good numerical algorithms for nonsymmetric eigenvalue problems also tend to be far more complex than their symmetric counterparts. This book deals with methods for solving a special nonsymmetric eig- value problem; the symplectic eigenvalue problem. The symplectic eigenvalue problem is helpful, e.g., in analyzing a number of different questions that arise in linear control theory for discrete-time systems. Certain quadratic eigenvalue problems arising, e.g., in finite element discretization in structural analysis, in acoustic simulation of poro-elastic materials, or in the elastic deformation of anisotropic materials can also lead to symplectic eigenvalue problems. The problem appears in other applications as well.

Author : Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel
Publisher : Springer
Page : 608 pages
File Size : 46,9 Mb
Release : 2015-05-09
Category : Mathematics
ISBN : 9783319152608

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Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory by Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel Pdf

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.

Author : David S. Watkins
Publisher : SIAM
Page : 443 pages
File Size : 52,7 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 9780898716412

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The Matrix Eigenvalue Problem by David S. Watkins Pdf

An in-depth, theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems.

Author : Leslie Hogben
Publisher : CRC Press
Page : 1838 pages
File Size : 40,7 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9781466507296

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Handbook of Linear Algebra by Leslie Hogben Pdf

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

Author : Wan-Xie Zhong
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 53,5 Mb
Release : 2006-04-11
Category : Mathematics
ISBN : 9781402078811

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Duality System in Applied Mechanics and Optimal Control by Wan-Xie Zhong Pdf

A unified approach is proposed for applied mechanics and optimal control theory. The Hamilton system methodology in analytical mechanics is used for eigenvalue problems, vibration theory, gyroscopic systems, structural mechanics, wave-guide, LQ control, Kalman filter, robust control etc. All aspects are described in the same unified methodology. Numerical methods for all these problems are provided and given in meta-language, which can be implemented easily on the computer. Precise integration methods both for initial value problems and for two-point boundary value problems are proposed, which result in the numerical solutions of computer precision. Key Features of the text include: -Unified approach based on Hamilton duality system theory and symplectic mathematics. -Gyroscopic system vibration, eigenvalue problems. -Canonical transformation applied to non-linear systems. -Pseudo-excitation method for structural random vibrations. -Precise integration of two-point boundary value problems. -Wave propagation along wave-guides, scattering. -Precise solution of Riccati differential equations. -Kalman filtering. -HINFINITY theory of control and filter.

Author : Biswa Datta
Publisher : Academic Press
Page : 737 pages
File Size : 41,8 Mb
Release : 2004
Category : Mathematics
ISBN : 9780122035906

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Numerical Methods for Linear Control Systems by Biswa Datta Pdf

Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions Background material in linear algebra, numerical linear algebra, and control theory included in text Step-by-step explanations of the algorithms and examples

Author : Felipe Cucker
Publisher : Cambridge University Press
Page : 218 pages
File Size : 41,5 Mb
Release : 2004-03-25
Category : Mathematics
ISBN : 0521542537

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Foundations of Computational Mathematics, Minneapolis 2002 by Felipe Cucker Pdf

This volume, first published in 2004, contains the plenary invited talks given at main conference in the subject.

Author : Daniel Kressner
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 42,9 Mb
Release : 2006-01-20
Category : Mathematics
ISBN : 9783540285021

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Numerical Methods for General and Structured Eigenvalue Problems by Daniel Kressner Pdf

This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.

Author : Moody Chu,Gene Golub
Publisher : Oxford University Press
Page : 408 pages
File Size : 44,9 Mb
Release : 2005-06-16
Category : Mathematics
ISBN : 9780198566649

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Inverse Eigenvalue Problems by Moody Chu,Gene Golub Pdf

Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.

Author : Philipp Hennig,Michael A. Osborne,Hans P. Kersting
Publisher : Cambridge University Press
Page : 411 pages
File Size : 45,6 Mb
Release : 2022-06-30
Category : Computers
ISBN : 9781107163447

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Probabilistic Numerics by Philipp Hennig,Michael A. Osborne,Hans P. Kersting Pdf

A thorough introduction to probabilistic numerics showing how to build more flexible, efficient, or customised algorithms for computation.

Author : Anonim
Publisher : Unknown
Page : 410 pages
File Size : 50,6 Mb
Release : 2000
Category : Computers
ISBN : UOM:39015049121117

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BIT. by Anonim Pdf

Author : Walter Gautschi
Publisher : Springer Science & Business Media
Page : 611 pages
File Size : 53,8 Mb
Release : 2011-12-06
Category : Mathematics
ISBN : 9780817682590

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Numerical Analysis by Walter Gautschi Pdf

Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.

Author : Philip Saltenberger
Publisher : Logos Verlag Berlin GmbH
Page : 191 pages
File Size : 53,6 Mb
Release : 2019-05-30
Category : Mathematics
ISBN : 9783832549145

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On different concepts for the linearization of matrix polynomials and canonical decompositions of structured matrices with respect to indefinite sesquilinear forms by Philip Saltenberger Pdf

In this thesis, a novel framework for the construction and analysis of strong linearizations for matrix polynomials is presented. Strong linearizations provide the standard means to transform polynomial eigenvalue problems into equivalent generalized eigenvalue problems while preserving the complete finite and infinite eigenstructure of the problem. After the transformation, the QZ algorithm or special methods appropriate for structured linearizations can be applied for finding the eigenvalues efficiently. The block Kronecker ansatz spaces proposed here establish an innovative and flexible approach for the construction of strong linearizations in the class of strong block minimal bases pencils. Moreover, they represent a new vector-space-setting for linearizations of matrix polynomials that additionally provides a common basis for various existing techniques on this task (such as Fiedler-linearizations). New insights on their relations, similarities and differences are revealed. The generalized eigenvalue problems obtained often allow for an efficient numerical solution. This is discussed with special attention to structured polynomial eigenvalue problems whose linearizations are structured as well. Structured generalized eigenvalue problems may also lead to equivalent structured (standard) eigenvalue problems. Thereby, the transformation produces matrices that can often be regarded as selfadjoint or skewadjoint with respect to some indefinite inner product. Based on this observation, normal matrices in indefinite inner product spaces and their spectral properties are studied and analyzed. Multiplicative and additive canonical decompositions respecting the matrix structure induced by the inner product are established.

Author : Achim Ilchmann,Timo Reis
Publisher : Springer
Page : 313 pages
File Size : 40,5 Mb
Release : 2015-10-29
Category : Mathematics
ISBN : 9783319224282

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Surveys in Differential-Algebraic Equations III by Achim Ilchmann,Timo Reis Pdf

The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Flexibility of DAE formulations - Reachability analysis and deterministic global optimization - Numerical linear algebra methods - Boundary value problems The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

Author : Noor Ahmed
Publisher : BoD – Books on Demand
Page : 258 pages
File Size : 54,7 Mb
Release : 2016-10-05
Category : Technology & Engineering
ISBN : 9789535126744

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Advances in Noise Analysis, Mitigation and Control by Noor Ahmed Pdf

The adverse impacts from excess noise on human health and daily activities have accelerated at an alarming rate over the last few decades. This has prompted significant research into noise attenuation and mitigation of these unwanted effects. This book is a collection of works from eminent researchers from around the world, who address the aforementioned issues. It provides the most up-to-date information on current work being conducted in the field of noise pollution and is of value to a wide range of students, engineers, scientists and industry consultants who wish to further understand current methodologies and emerging concepts.