Some new and simple Gramian-based model order reduction algorithms are presented on second-order linear dynamical\r\nsystems, namely, SVD methods. Compared to existing Gramian-based algorithms, that is, balanced truncation methods, they\r\nare competitive and more favorable for large-scale systems. Numerical examples show the validity of the algorithms. Error bounds\r\non error systems are discussed. Some observations are given on structures of Gramians of second order linear systems.
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