Titlebook: Dimension Reduction of Large-Scale Systems; Proceedings of a Wor Peter Benner,Danny C. Sorensen,Volker Mehrmann Conference proceedings 2005

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Conference proceedings 2005isting and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines..

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Model Reduction Based on Spectral Projection Methodstional tool of most of the discussed algorithms for computing reduced-order models. Implementations for large-scale problems based on parallelization or formatted arithmetic will also be discussed. This chapter can also serve as a tutorial on Gramian-based model reduction using spectral projection methods.

DUST

Controller Reduction Using Accuracy-Enhancing Methodsility and observability Gramians can be achieved by solving reduced order Lyapunov equations. All discussed approaches can be used in conjunction with square-root and balancing-free accuracy enhancing techniques. For a selected class of methods robust numerical software is available.

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Model Reduction Based on Spectral Projection Methodson techniques, employing the idea of spectral projection. Mostly, we will be concerned with the sign function method which serves as the major computational tool of most of the discussed algorithms for computing reduced-order models. Implementations for large-scale problems based on parallelization

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Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Formirst give a brief overview of the basic concepts from linear system theory and then present balanced truncation model reduction methods for descriptor systems and discuss their algorithmic aspects. The efficiency of these methods is demonstrated by numerical experiments.

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Padé-Type Model Reduction of Second-Order and Higher-Order Linear Dynamical Systemsd then employ Krylov-subspace techniques for reduced-order modeling of first-order systems. While this approach results in reduced-order models that are characterized as Padé-type or even true Padé approximants of the system‘s transfer function, in general, these models do not preserve the form of t

parsimony

Controller Reduction Using Accuracy-Enhancing Methodss is considered. For certain categories of performance and stability enforcing frequency-weights, the computation of the frequency-weighted controllability and observability Gramians can be achieved by solving reduced order Lyapunov equations. All discussed approaches can be used in conjunction with

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