Browsing by Author "Gugercin, S."

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    A Modified Low-Rank Smith Method for Large-Scale Lyapunov Equations
    (2001-05) Antoulas, A.C.; Sorensen, D.C.; Gugercin, S.
    In this note we present a modified cyclic low-rank Smith method to compute low-rank approximations to solutions of Lyapunov equations arising from large-scale dynamical systems. Unlike the original cyclic low-rank Smith method introduced by Penzl in [18], the number of the columns in the approximate solutions does not necessarily increase at each step. The number of columns required by the modified method is usually much lower than the original cyclic low-rank Smith method. The modified method never requires more columns than the original. Upper bounds are established for the errors in the low-rank approximate solutions and also for the errors in the resulting approximate Hankel singular values. Numerical results are given to verify the efficiency and accuracy of the new algorithm.
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    A Survey of Model Reduction Methods for Large-Scale Systems
    (2000-12) Antoulas, A.C.; Sorensen, D.C.; Gugercin, S.
    An overview of model reduction methods and a comparison of the resulting algorithms are presented. These approaches are divided into two broad categories, namely SVD based and moment matching based methods. It turns out that the approximation error in the former case behaves better globally in frequency while in the latter case the local behavior is better.