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

• URL: http://arxiv.org/abs/2411.02333v1
• Date: Mon, 04 Nov 2024 17:58:31 GMT
• Title: Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula
• Authors: Jiakuang He, Dongqing Wu,
• Abstract summary: Time-variant 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. Based on Euler-forward formula discretion, Con-DZND1-2i model and Con-DZND2-2i model are proposed.
• Score: 1.1970409518725493
• License:
• Abstract: 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.

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