Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
SIAM Journal on Matrix Analysis and Applications
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Dealing with large scale dynamical systems is important in many industrial applications. In design and optimization, it is often impossible to work with the original large scale system due to the necessary time for simulation. In order to make this process economically acceptable one has to replace these large scale models by smaller ones which preserve the essential properties and dynamics of the original one. After the computation of a reduced order model a fast simulation is possible. The reduced order model can be obtained by different techniques minimizing the reduction error with respect to different system norms. One of the most common techniques in this application area is balanced truncation [8] which approximates with respect to the $\mathcal{H}_\infty$-norm. A parallel implementation of this is available in PLiCMR [2]. In this contribution we focus on the parallel implementation of the IRKA algorithm employing the $\mathcal{H}_2$-norm [1,11] for measuring the error.