Browsing by Author "Antoulas, Athanasios C."

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    H2 model reduction for large-scale linear dynamical systems
    Gugercin, Serkan; Antoulas, Athanasios C.; Beattie, Christopher A. (Siam Publications, 2008)
    The optimal H2 model reduction problem is of great importance in the area of dynamical systems and simulation. In the literature, two independent frameworks have evolved focusing either on solution of Lyapunov equations on the one hand or interpolation of transfer functions on the other, without any apparent connection between the two approaches. In this paper, we develop a new unifying framework for the optimal H2 approximation problem using best approximation properties in the underlying Hilbert space. This new framework leads to a new set of local optimality conditions taking the form of a structured orthogonality condition. We show that the existing Lyapunov- and interpolation-based conditions are each equivalent to our conditions and so are equivalent to each other. Also, we provide a new elementary proof of the interpolation-based condition that clarifies the importance of the mirror images of the reduced system poles. Based on the interpolation framework, we describe an iteratively corrected rational Krylov algorithm for H2 model reduction. The formulation is based on finding a reduced order model that satisfies interpolation-based first-order necessary conditions for H2 optimality and results in a method that is numerically effective and suited for large-scale problems. We illustrate the performance of the method with a variety of numerical experiments and comparisons with existing methods.
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    Interpolatory weighted-H-2 model reduction
    Anic, Branimir; Beattie, Christopher A.; Gugercin, Serkan; Antoulas, Athanasios C. (Pergamon-Elsevier, 2013-05-01)
    This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an optimal reduced-order model. The H2 norm representation also provides an error expression that motivates a new weighted-H2 model reduction algorithm. Several numerical examples illustrate the effectiveness of the proposed approach.