Low-rank alternating direction doubling algorithm for solving large-scale continuous time algebraic Riccati equations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913323104075776 |
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| author | Zhang, Juan Xun, Wenlu |
| author_facet | Zhang, Juan Xun, Wenlu |
| contents | This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the alternating direction doubling algorithm (ADDA), utilizing the low-rank property of matrices and employing Cholesky factorization for solving. The advantage of the new algorithm lies in computing only the $2^k$-th approximation during the iterative process, instead of every approximation. Its efficient low-rank formula saves storage space and is highly effective from a computational perspective. Finally, the effectiveness of the new algorithm is demonstrated through theoretical analysis and numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12155 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Low-rank alternating direction doubling algorithm for solving large-scale continuous time algebraic Riccati equations Zhang, Juan Xun, Wenlu Numerical Analysis This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the alternating direction doubling algorithm (ADDA), utilizing the low-rank property of matrices and employing Cholesky factorization for solving. The advantage of the new algorithm lies in computing only the $2^k$-th approximation during the iterative process, instead of every approximation. Its efficient low-rank formula saves storage space and is highly effective from a computational perspective. Finally, the effectiveness of the new algorithm is demonstrated through theoretical analysis and numerical experiments. |
| title | Low-rank alternating direction doubling algorithm for solving large-scale continuous time algebraic Riccati equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.12155 |