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The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.

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The goal of this book is three-fold: it describes the basics of model order reduction and related aspects. In numerical linear algebra, it covers both general and more specialized model order reduction techniques for linear and nonlinear systems, and it discusses the use of model order reduction techniques in a variety of practical applications. The book contains many recent advances in model order reduction, and presents several open problems for which techniques are still in development. It will serve as a source of inspiration for its readers, who will discover that model order reduction is a very exciting and lively field.

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Differential equations --- Boundary value problems --- Nonlinear boundary value problems --- Initial value problems --- Équations différentielles --- Problèmes aux limites --- Problèmes aux limites non linéaires --- Problèmes aux valeurs initiales --- Numerical solutions --- Solutions numériques --- Problèmes aux limites. --- Problèmes aux limites non linéaires. --- Problèmes aux valeurs initiales. --- Solutions numériques. --- Équations différentielles --- Problèmes aux limites. --- Problèmes aux limites non linéaires. --- Problèmes aux valeurs initiales. --- Solutions numériques.

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An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.

MATHEMATICS / Numerical Analysis.