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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/2408.14057 |
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| _version_ | 1866909295799435264 |
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| author | He, Jiakuang Wu, Dongqing |
| author_facet | He, Jiakuang Wu, Dongqing |
| contents | Large-scale linear equations and high dimension have been hot topics in deep learning, machine learning, control,and scientific computing. Because of special conjugate operation characteristics, time-variant complex conjugate matrix equations need to be transformed into corresponding real field time-variant large-scale linear equations. In this paper, zeroing neural dynamic models based on complex field error (called Con-CZND1) and based on real field error (called Con-CZND2) are proposed for in-depth analysis. Con-CZND1 has fewer elements because of the direct processing of complex matrices. Con-CZND2 needs to be transformed into the real field, with more elements, and its performance is affected by the main diagonal dominance of coefficient matrices. A neural hypercomplex numbers space compressive approximation approach (NHNSCAA) is innovatively proposed. Then Con-CZND1 conj model is constructed. Numerical experiments verify Con-CZND1 conj model effectiveness and highlight NHNSCAA importance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14057 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting time-variant complex conjugate matrix equations with their corresponding real field time-variant large-scale linear equations, neural hypercomplex numbers space compressive approximation approach He, Jiakuang Wu, Dongqing Numerical Analysis Distributed, Parallel, and Cluster Computing Neural and Evolutionary Computing Systems and Control Chaotic Dynamics Large-scale linear equations and high dimension have been hot topics in deep learning, machine learning, control,and scientific computing. Because of special conjugate operation characteristics, time-variant complex conjugate matrix equations need to be transformed into corresponding real field time-variant large-scale linear equations. In this paper, zeroing neural dynamic models based on complex field error (called Con-CZND1) and based on real field error (called Con-CZND2) are proposed for in-depth analysis. Con-CZND1 has fewer elements because of the direct processing of complex matrices. Con-CZND2 needs to be transformed into the real field, with more elements, and its performance is affected by the main diagonal dominance of coefficient matrices. A neural hypercomplex numbers space compressive approximation approach (NHNSCAA) is innovatively proposed. Then Con-CZND1 conj model is constructed. Numerical experiments verify Con-CZND1 conj model effectiveness and highlight NHNSCAA importance. |
| title | Revisiting time-variant complex conjugate matrix equations with their corresponding real field time-variant large-scale linear equations, neural hypercomplex numbers space compressive approximation approach |
| topic | Numerical Analysis Distributed, Parallel, and Cluster Computing Neural and Evolutionary Computing Systems and Control Chaotic Dynamics |
| url | https://arxiv.org/abs/2408.14057 |