Model Reduction and Approximation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Model Reduction and Approximation write by Peter Benner. This book was released on 2017-07-06. Model Reduction and Approximation available in PDF, EPUB and Kindle. Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.
Interpolatory Methods for Model Reduction
Interpolatory Methods for Model Reduction - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Interpolatory Methods for Model Reduction write by A. C. Antoulas. This book was released on 2020-01-13. Interpolatory Methods for Model Reduction available in PDF, EPUB and Kindle. Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.
Model Order Reduction: Theory, Research Aspects and Applications
Model Order Reduction: Theory, Research Aspects and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Model Order Reduction: Theory, Research Aspects and Applications write by Wilhelmus H. Schilders. This book was released on 2008-08-27. Model Order Reduction: Theory, Research Aspects and Applications available in PDF, EPUB and Kindle. The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.
Model Reduction for Control System Design
Model Reduction for Control System Design - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Model Reduction for Control System Design write by Goro Obinata. This book was released on 2012-12-06. Model Reduction for Control System Design available in PDF, EPUB and Kindle. Comprehensive treatment of approximation methods for filters and controllers. It is fully up to date, and it is authored by two leading researchers who have personally contributed to the development of some of the methods. Balanced truncation, Hankel norm reduction, multiplicative reduction, weighted methods and coprime factorization methods are all discussed. The book is amply illustrated with examples, and will equip practising control engineers and graduates for intelligent use of commercial software modules for model and controller reduction.
Approximation of Large-Scale Dynamical Systems
Approximation of Large-Scale Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Approximation of Large-Scale Dynamical Systems write by Athanasios C. Antoulas. This book was released on 2009-06-25. Approximation of Large-Scale Dynamical Systems available in PDF, EPUB and Kindle. 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.
