Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula
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.
Cite
@article{arxiv.2411.02333,
title = {Discrete the solving model of time-variant standard Sylvester-conjugate matrix equations using Euler-forward formula},
author = {Jiakuang He and Dongqing Wu},
journal= {arXiv preprint arXiv:2411.02333},
year = {2024}
}
Comments
An analysis of the differences between sampling discretion errors and space compressive approximation errors in optimizing neural dynamics