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Model Reduction and Approximation: Theory and Algorithms

Edited by Peter Benner, Albert Cohen, Mario Ohlberger, and Karen Willcox

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2017 / xxii + 412 pages / Softcover / ISBN 978-1-611974-81-2 / List Price $99.00 / SIAM Member Price$69.30 / Order Code: CS15

Keywords: model reduction, approximation, proper orthogonal decomposition, reduced basis method, tensor methods

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;
• is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods; and
• covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).

Audience
This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.