An RADI-type method for stochastic continuous-time algebraic Riccati equations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916446890622976 |
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| author | Guo, Zhen-Chen Liang, Xin |
| author_facet | Guo, Zhen-Chen Liang, Xin |
| contents | In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-type methods is developed by integrating the core concept of the original RADI method with the implicit appearance of the left semi-tensor product in stochastic continuous-time algebraic Riccati equations.The method employs different shifts to accelerate convergence and uses compression techniques to reduce storage requirements and computational complexity.Unlike many existing methods for large-scale problems such as Newton-type methods and homotopy method, it calculates the residual at a low cost and does not require a stabilizing initial approximation, which can often be challenging to find. Numerical experiments are provided to demonstrate its efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An RADI-type method for stochastic continuous-time algebraic Riccati equations Guo, Zhen-Chen Liang, Xin Numerical Analysis Optimization and Control 65F45, 15A24 In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-type methods is developed by integrating the core concept of the original RADI method with the implicit appearance of the left semi-tensor product in stochastic continuous-time algebraic Riccati equations.The method employs different shifts to accelerate convergence and uses compression techniques to reduce storage requirements and computational complexity.Unlike many existing methods for large-scale problems such as Newton-type methods and homotopy method, it calculates the residual at a low cost and does not require a stabilizing initial approximation, which can often be challenging to find. Numerical experiments are provided to demonstrate its efficiency. |
| title | An RADI-type method for stochastic continuous-time algebraic Riccati equations |
| topic | Numerical Analysis Optimization and Control 65F45, 15A24 |
| url | https://arxiv.org/abs/2403.02940 |