Frequency- and time-limited balanced truncation for large-scale second-order systems
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefore, it usually pays off to compute local approximations of the used dynamical systems in the frequency and time domain. In this paper, we consider a...
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| Veröffentlicht in: | Linear algebra and its applications 2021-08, Vol.623, p.68-103 |
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| creator | Benner, Peter Werner, Steffen W.R. |
| description | Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefore, it usually pays off to compute local approximations of the used dynamical systems in the frequency and time domain. In this paper, we consider a structure-preserving extension of the frequency- and time-limited balanced truncation methods to second-order dynamical systems. We give a full overview about the first-order limited balanced truncation methods and extend those to second-order systems by using the different second-order balanced truncation formulas from the literature. Also, we present numerical methods for solving the arising large-scale sparse matrix equations and give numerical modifications to deal with the problematic case of second-order systems. The results are then illustrated on three numerical examples. |
| doi_str_mv | 10.1016/j.laa.2020.06.024 |
| format | Article |
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| ispartof | Linear algebra and its applications, 2021-08, Vol.623, p.68-103 |
| issn | 0024-3795 1873-1856 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Balanced truncation Dynamical systems Frequency-limited balanced truncation Linear algebra Linear systems Local model reduction Model order reduction Numerical methods Second-order differential equations Sparse matrices Structure-preserving approximation Time-limited balanced truncation |
| title | Frequency- and time-limited balanced truncation for large-scale second-order systems |
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