Antoulas A.C. Approximation of Large-Scale Dynamical Systems

Philadelphia: SIAM, 2005. — 508p.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. This book is for anyone interested in model reduction. Graduate students and researchers in the fields of system and control theory, numerical analysis, and the theory of partial differential equations/computational fluid dynamics will find it an excellent reference.List of Figures;
Foreword;
Preface;
How to Use this Book;Introduction;
Motivating Examples;
Preliminaries.
Tools from Matrix Theory;
Linear Dynamical Systems:
Sylvester and Lyapunov equations;
SVD-based Approximation Methods.
Balancing and balanced approximations;
Hankel-norm Approximation;
Special topics in SVD-based approximation methods;
Krylov-based Approximation Methods;
Eigenvalue Computations;
Model Reduction Using Krylov Methods;
SVD–Krylov Methods and Case Studies.
SVD–Krylov Methods;
Case Studies;
Epilogue;
Problems;
Bibliography;