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
<|reference_start|>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: 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.<|reference_end|>
@article{he2024revisiting,
    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},
    author={Jiakuang He, Dongqing Wu},
    journal={arXiv preprint arXiv:2408.14057},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.14057},
    primaryClass={math.NA cs.DC cs.NA cs.NE cs.SY eess.SY nlin.CD}
}