Symplectic Methods for the Symplectic Eigenproblem (Hardcover)

Heike Fassbender

ISBN 10: 0306464780 / ISBN 13: 9780306464782

Published by Springer Science+Business Media, New York, 2000

Hardcover. The symplectic eigenvalue problem is helpful in analyzing a number of different questions that arise in linear control theory for discrete-time systems. Industrial production and technological processes may suffer from unwanted behaviour, for example, losses in the start-up and change-over phases of operation, pollution, emission of harmful elements, and production of unwanted by-products. Control techniques offer the possibility of analyzing such processes in order to detect the underlying causes of the unwanted behaviour. This monograph describes techniques for solving small to medium-sized as well as large and sparse symplectic eigenvalue problems. The text presents all developed algorithms in Matlab-programming style and numerical examples to demonstrate their abilities, all of which makes the text accessible to graduate students in applied mathematics and control engineering, as well as to researchers in these areas. This monograph describes techniques for solving small to medium-sized as well as large and sparse symplectic eigenvalue problems. The text presents all developed algorithms in Matlab-programming style and numerical examples to demonstrate their abilities. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780306464782

Synopsis:

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.

Bibliographic Details

Title: Symplectic Methods for the Symplectic ...
Publisher: Springer Science+Business Media, New York
Publication Date: 2000
Binding: Hardcover
Condition: new