Symplectic Methods for the Symplectic Eigenproblem by Heike FassbenderSymplectic Methods for the Symplectic Eigenproblem by Heike Fassbender

Symplectic Methods for the Symplectic Eigenproblem

byHeike Fassbender

Hardcover | November 30, 2000

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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.
Title:Symplectic Methods for the Symplectic EigenproblemFormat:HardcoverDimensions:269 pagesPublished:November 30, 2000Publisher:Kluwer Boston Inc.Language:English

The following ISBNs are associated with this title:

ISBN - 10:0306464780

ISBN - 13:9780306464782


Table of Contents

List of Figures. List of Tables. Acknowledgments. 1. Introduction. 2. Preliminaries. 3. The Butterfly Form for Symplectic Matrices and Matrix Pencils. 4. Butterfly SR and SZ Algorithms. 5. The Symplectic Lanczos Algorithm. 6. Concluding Remarks.