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Main Authors: He, Jiakuang, Wu, Dongqing
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2406.12783
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author He, Jiakuang
Wu, Dongqing
author_facet He, Jiakuang
Wu, Dongqing
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_12783
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Zeroing neural dynamics solving time-variant complex conjugate matrix equation $X(τ)F(τ)-A(τ)\overline{X}(τ)=C(τ)$
He, Jiakuang
Wu, Dongqing
Neural and Evolutionary Computing
Distributed, Parallel, and Cluster Computing
Numerical Analysis
Systems and Control
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.
title Zeroing neural dynamics solving time-variant complex conjugate matrix equation $X(τ)F(τ)-A(τ)\overline{X}(τ)=C(τ)$
topic Neural and Evolutionary Computing
Distributed, Parallel, and Cluster Computing
Numerical Analysis
Systems and Control
url https://arxiv.org/abs/2406.12783