Approximation of Large-Scale Dynamical Systems

Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction.

Athanasios C. Antoulas (Author)

9780898716580, Society for Industrial and Applied Mathematics

Paperback / softback, published 25 June 2009

510 pages
25.3 x 17.4 x 2.4 cm, 0.89 kg

'… this book contains a wealth of useful information and is the most authoritative presentation of the approximation techniques for large-scale dynamical systems available at the moment. The book is highly recommended to graduate students and researchers in the fields of system and control theory, and numerical analysis.' Petko Petkov, Mathematical Reviews

Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.

Preface
Part I. Introduction: 1. Introduction
2. Motivating examples
Part II. Preliminaries: 3. Tools from matrix theory
4. Linear dynamical systems, Part 1
5. Linear dynamical systems, Part 2
6. Sylvester and Lyapunov equations
Part III. SVD-based Approximation Methods: 7. Balancing and balanced approximations
8. Hankel-norm approximation
9. Special topics in SVD-based approximation methods
Part IV. Krylov-based Approximation Methods: 10. Eigenvalue computations
11. Model reduction using Krylov methods
Part V. SVD-Krylov Methods and Case Studies: 12. SVD-Krylov methods
13. Case studies
14. Epilogue
15. Problems
Bibliography
Index.

Subject Areas: Nonlinear science [PBWR], Mathematical modelling [PBWH], Applied mathematics [PBW]