Adaptive low-rank exponential integrators for large-scale differential Riccati equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908917029666816 |
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| author | Li, Jinyi Li, Dongping Yang, Hua |
| author_facet | Li, Jinyi Li, Dongping Yang, Hua |
| contents | Matrix differential Riccati equation (DRE) typically exhibits transient and steady-state phases, posing challenges for fixed-step time integration methods, which may lack accuracy during transients or oversample in steady regimes. In this work, we propose adaptive low-rank matrix-valued exponential integrators for large-scale stiff DRE. The methods combine embedded exponential Rosenbrock-type schemes and adaptive step-size control, enabling an automatic adjustment to the evolving solution dynamics. This improves the accuracy during rapid transient phases while maintaining high accuracy in the steady state. Numerical experiments on benchmark problems demonstrate that the proposed adaptive integrators consistently improve accuracy and computational efficiency compared with fixed-step low-rank schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26429 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive low-rank exponential integrators for large-scale differential Riccati equation Li, Jinyi Li, Dongping Yang, Hua Numerical Analysis 65L05 Matrix differential Riccati equation (DRE) typically exhibits transient and steady-state phases, posing challenges for fixed-step time integration methods, which may lack accuracy during transients or oversample in steady regimes. In this work, we propose adaptive low-rank matrix-valued exponential integrators for large-scale stiff DRE. The methods combine embedded exponential Rosenbrock-type schemes and adaptive step-size control, enabling an automatic adjustment to the evolving solution dynamics. This improves the accuracy during rapid transient phases while maintaining high accuracy in the steady state. Numerical experiments on benchmark problems demonstrate that the proposed adaptive integrators consistently improve accuracy and computational efficiency compared with fixed-step low-rank schemes. |
| title | Adaptive low-rank exponential integrators for large-scale differential Riccati equation |
| topic | Numerical Analysis 65L05 |
| url | https://arxiv.org/abs/2603.26429 |