arXiv subjects

Dongqing Wu

Publications and source records attributed to Dongqing Wu.

3 recordsLinked to original sources

arXiv2026

Zeroing neural dynamics solving time-variant complex conjugate matrix equation $X(τ)F(τ)-A(τ)\overline{X}(τ)=C(τ)$

Complex conjugate matrix equations (CCME) are important in computation and antilinear systems. Existing research mainly focuses on the time-invariant version, while studies on the time-variant version and its solution using artificial neural networks are still lacking. This paper introduces zeroing neural dynamics (ZND) to solve the earliest time-variant CCME. Firstly, the vectorization and Kronecker product in the complex field are defined uniformly. Secondly, Con-CZND1 and Con-CZND2 models are proposed, and their convergence and effectiveness are theoretically proved. Thirdly, numerical experiments confirm their effectiveness and highlight their differences. The results show the advantages of ZND in the complex field compared with that in the real field, and further refine the related theory.

cs.NE↗

arXiv2024

Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula

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.

math.NA↗

arXiv2024

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.

math.NA↗