Cross-Gramian-Based Model Reduction for Descriptor Systems
In this paper, we explore model order reduction for large-scale square descriptor systems. A balancing-free square-root method is proposed. The balancing-free square-root method is based on two cross Gramians, one of which is known as the proper cross Gramian and the other as the improper cross Gram...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2400 |
| _version_ | 1797463900239691776 |
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| author | Yiqin Lin |
| author_facet | Yiqin Lin |
| author_sort | Yiqin Lin |
| collection | DOAJ |
| description | In this paper, we explore model order reduction for large-scale square descriptor systems. A balancing-free square-root method is proposed. The balancing-free square-root method is based on two cross Gramians, one of which is known as the proper cross Gramian and the other as the improper cross Gramian. The proper cross Gramian is the unique solution of a projected generalized continuous-time Sylvester equation, and the improper cross Gramian solves a projected generalized discrete-time Sylvester equation. In order to compute the low-rank factors of these two cross Gramians, we extend the low-rank iteration of the alternating direction implicit method and the Smith method to the projected generalized Sylvester equations. We illustrate the effectiveness of the balance truncation method with one numerical example. |
| first_indexed | 2024-03-09T17:57:19Z |
| format | Article |
| id | doaj.art-9183db824e6449c8ad9bf0d271db3e49 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T17:57:19Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9183db824e6449c8ad9bf0d271db3e492023-11-24T10:13:25ZengMDPI AGSymmetry2073-89942022-11-011411240010.3390/sym14112400Cross-Gramian-Based Model Reduction for Descriptor SystemsYiqin Lin0School of Science, Hunan University of Science and Engineering, Yongzhou 425199, ChinaIn this paper, we explore model order reduction for large-scale square descriptor systems. A balancing-free square-root method is proposed. The balancing-free square-root method is based on two cross Gramians, one of which is known as the proper cross Gramian and the other as the improper cross Gramian. The proper cross Gramian is the unique solution of a projected generalized continuous-time Sylvester equation, and the improper cross Gramian solves a projected generalized discrete-time Sylvester equation. In order to compute the low-rank factors of these two cross Gramians, we extend the low-rank iteration of the alternating direction implicit method and the Smith method to the projected generalized Sylvester equations. We illustrate the effectiveness of the balance truncation method with one numerical example.https://www.mdpi.com/2073-8994/14/11/2400model reductioncross Gramianbalanced truncationprojected generalized Sylvester equationdescriptor system |
| spellingShingle | Yiqin Lin Cross-Gramian-Based Model Reduction for Descriptor Systems Symmetry model reduction cross Gramian balanced truncation projected generalized Sylvester equation descriptor system |
| title | Cross-Gramian-Based Model Reduction for Descriptor Systems |
| title_full | Cross-Gramian-Based Model Reduction for Descriptor Systems |
| title_fullStr | Cross-Gramian-Based Model Reduction for Descriptor Systems |
| title_full_unstemmed | Cross-Gramian-Based Model Reduction for Descriptor Systems |
| title_short | Cross-Gramian-Based Model Reduction for Descriptor Systems |
| title_sort | cross gramian based model reduction for descriptor systems |
| topic | model reduction cross Gramian balanced truncation projected generalized Sylvester equation descriptor system |
| url | https://www.mdpi.com/2073-8994/14/11/2400 |
| work_keys_str_mv | AT yiqinlin crossgramianbasedmodelreductionfordescriptorsystems |