Approximation of Large-Scale Dynamical Systems
Approximation of Large-Scale Dynamical Systems
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.
- Suitable for anyone interested in model reduction
- An excellent reference for graduate students and researchers in the fields of system and control theory, numerical analysis, and the theory of partial differential equations/computational fluid dynamics
- Provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations
Reviews & endorsements
'… 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
Product details
No date availablePaperback
9780898716580
510 pages
253 × 174 × 24 mm
0.89kg
Table of Contents
- 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.
