Hamiltonian And Gradient Flows Algorithms And Control

Author : Anthony Bloch
Publisher : American Mathematical Soc.
ISBN 13 : 0821802550
Total Pages : 166 pages
Book Rating : 4.57/5 ( download)

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Download or read book Hamiltonian and Gradient Flows, Algorithms and Control written by Anthony Bloch and published by American Mathematical Soc.. This book was released on 1994 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together ideas from several areas of mathematics that have traditionally been rather disparate. The conference at the Fields Institute which gave rise to these proceedings was intended to enourage such connections. One of the key interactions occurs between dynamical systems and algorithms, one example being the by now classic observation that the QR algorithm for diagonalizing matrices may be viewed as the time-1 map of the Toda lattice flow. Another link occurs with interior point methods for linear programming, where certain smooth flows associated with such programming problems have proved valuable in the analysis of the corresponding discrete problems. More recently, other smooth flows have been introduced which carry out discrete computations (such as sorting sets of numbers) and which solve certain least squares problems. Another interesting facet of the flows described here is that they often have a dual Hamiltonian and gradient structure, both of which turn out to be useful in analysing and designing algorithms for solving optimization problems. This volume explores many of these interactions, as well as related work in optimal control and partial differential equations.

Author :
Publisher :
ISBN 13 : 9781470429713
Total Pages : pages
Book Rating : 4.13/5 ( download)

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Download or read book Hamiltonian and Gradient Flows, Algorithms, and Control written by and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together ideas from several areas of mathematics that have traditionally been rather disparate. The conference at The Fields Institute which gave rise to these proceedings was intended to encourage such connections. One of the key interactions occurs between dynamical systems and algorithms, one example being the by now classic observation that the QR algorithm for diagonalizing matrices may be viewed as the time-1 map of the Toda lattice flow. Another link occurs with interior point methods for linear programming, where certain smooth flows associated with such programming.

Author : Anthony Bloch
Publisher : American Mathematical Soc.
ISBN 13 : 9780821871362
Total Pages : 172 pages
Book Rating : 4.66/5 ( download)

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Download or read book Hamiltonian and Gradient Flows, Algorithms, and Control written by Anthony Bloch and published by American Mathematical Soc.. This book was released on with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of a conference held at the Fields Insitute and designed to bring together traditionally disparate fields of mathematical research. On such key interraction occurs between dynamical systems and algorithms. This volume explores many such interractions as well as related work in optimal control and partial differential equations.

Author : John B. Baillieul
Publisher : Springer Science & Business Media
ISBN 13 : 1461214165
Total Pages : 389 pages
Book Rating : 4.68/5 ( download)

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Download or read book Mathematical Control Theory written by John B. Baillieul and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume on mathematical control theory contains high quality articles covering the broad range of this field. The internationally renowned authors provide an overview of many different aspects of control theory, offering a historical perspective while bringing the reader up to the very forefront of current research.

Author : Vladimir G. Ivancevic
Publisher : World Scientific
ISBN 13 : 981442594X
Total Pages : 737 pages
Book Rating : 4.40/5 ( download)

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Download or read book New Trends in Control Theory written by Vladimir G. Ivancevic and published by World Scientific. This book was released on 2013 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Trends in Control Theory is a graduate-level monographic textbook. It is a contemporary overview of modern trends in control theory. The introductory chapter gives the geometrical and quantum background, which is a necessary minimum for comprehensive reading of the book. The second chapter gives the basics of classical control theory, both linear and nonlinear. The third chapter shows the key role that Euclidean group of rigid motions plays in modern robotics and biomechanics. The fourth chapter gives an overview of modern quantum control, from both theoretical and measurement perspectives. The fifth chapter presents modern control and synchronization methods in complex systems and human crowds. The appendix provides the rest of the background material complementary to the introductory chapter. The book is designed as a one-semester course for engineers, applied mathematicians, computer scientists and physicists, both in industry and academia. It includes a most relevant bibliography on the subject and detailed index.

Author : Andreas Johann
Publisher : Springer Science & Business Media
ISBN 13 : 3034804512
Total Pages : 628 pages
Book Rating : 4.16/5 ( download)

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Download or read book Recent Trends in Dynamical Systems written by Andreas Johann and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.

Author : Heike Fassbender
Publisher : Springer Science & Business Media
ISBN 13 : 0306469782
Total Pages : 277 pages
Book Rating : 4.87/5 ( download)

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Download or read book Symplectic Methods for the Symplectic Eigenproblem written by Heike Fassbender and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Loyce M. Adams
Publisher : SIAM
ISBN 13 : 9780898713763
Total Pages : 186 pages
Book Rating : 4.65/5 ( download)

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Download or read book Linear and Nonlinear Conjugate Gradient-related Methods written by Loyce M. Adams and published by SIAM. This book was released on 1996-01-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the AMS-IMS-SIAM Summer Research Conference held at the University of Washington, July 1995.

Author : Fritz Gesztesy
Publisher : Cambridge University Press
ISBN 13 : 1139473778
Total Pages : 438 pages
Book Rating : 4.74/5 ( download)

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Download or read book Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models written by Fritz Gesztesy and published by Cambridge University Press. This book was released on 2008-09-04 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

Author : Raf Vandebril
Publisher : JHU Press
ISBN 13 : 0801896800
Total Pages : 516 pages
Book Rating : 4.04/5 ( download)

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Download or read book Matrix Computations and Semiseparable Matrices written by Raf Vandebril and published by JHU Press. This book was released on 2008-12-15 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general properties and mathematical structures of semiseparable matrices were presented in volume 1 of Matrix Computations and Semiseparable Matrices. In volume 2, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi discuss the theory of structured eigenvalue and singular value computations for semiseparable matrices. These matrices have hidden properties that allow the development of efficient methods and algorithms to accurately compute the matrix eigenvalues. This thorough analysis of semiseparable matrices explains their theoretical underpinnings and contains a wealth of information on implementing them in practice. Many of the routines featured are coded in Matlab and can be downloaded from the Web for further exploration.