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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.02333 |
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| _version_ | 1866913571302014976 |
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| author | He, Jiakuang Wu, Dongqing |
| author_facet | He, Jiakuang Wu, Dongqing |
| contents | Time-variant standard Sylvester-conjugate matrix equations are presented as early time-variant versions of the complex conjugate matrix equations. Current solving methods include Con-CZND1 and Con-CZND2 models, both of which use ode45 for continuous model. Given practical computational considerations, discrete these models is also important. Based on Euler-forward formula discretion, Con-DZND1-2i model and Con-DZND2-2i model are proposed. Numerical experiments using step sizes of 0.1 and 0.001. The above experiments show that Con-DZND1-2i model and Con-DZND2-2i model exhibit different neural dynamics compared to their continuous counterparts, such as trajectory correction in Con-DZND2-2i model and the swallowing phenomenon in Con-DZND1-2i model, with convergence affected by step size. These experiments highlight the differences between optimizing sampling discretion errors and space compressive approximation errors in neural dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula He, Jiakuang Wu, Dongqing Numerical Analysis Distributed, Parallel, and Cluster Computing Neural and Evolutionary Computing Systems and Control Mathematical Physics Time-variant standard Sylvester-conjugate matrix equations are presented as early time-variant versions of the complex conjugate matrix equations. Current solving methods include Con-CZND1 and Con-CZND2 models, both of which use ode45 for continuous model. Given practical computational considerations, discrete these models is also important. Based on Euler-forward formula discretion, Con-DZND1-2i model and Con-DZND2-2i model are proposed. Numerical experiments using step sizes of 0.1 and 0.001. The above experiments show that Con-DZND1-2i model and Con-DZND2-2i model exhibit different neural dynamics compared to their continuous counterparts, such as trajectory correction in Con-DZND2-2i model and the swallowing phenomenon in Con-DZND1-2i model, with convergence affected by step size. These experiments highlight the differences between optimizing sampling discretion errors and space compressive approximation errors in neural dynamics. |
| title | Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula |
| topic | Numerical Analysis Distributed, Parallel, and Cluster Computing Neural and Evolutionary Computing Systems and Control Mathematical Physics |
| url | https://arxiv.org/abs/2411.02333 |