From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique

The time-variant matrix inversion (TVMI) problem solving is the hotspot of current research because of its frequent appearance and application in scientific research and industrial production. The generalized inverse problem of singular square matrix and nonsquare matrix can be related to Penrose eq...

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Autores principales:	Dongqing Wu, Yunong Zhang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/cb87b135b2604947a4064b98ed7ff6f1
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id	oai:doaj.org-article:cb87b135b2604947a4064b98ed7ff6f1
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spelling	oai:doaj.org-article:cb87b135b2604947a4064b98ed7ff6f12021-11-29T00:56:31ZFrom Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique1607-887X10.1155/2021/4227512https://doaj.org/article/cb87b135b2604947a4064b98ed7ff6f12021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/4227512https://doaj.org/toc/1607-887XThe time-variant matrix inversion (TVMI) problem solving is the hotspot of current research because of its frequent appearance and application in scientific research and industrial production. The generalized inverse problem of singular square matrix and nonsquare matrix can be related to Penrose equations (PEs). The PEs implicitly define the generalized inverse of a known matrix, which is of fundamental theoretical significance. Therefore, the in-depth study of PEs might enlighten problem solving of TVMI in a foreseeable way. For the first time, we construct three different matrix error-monitoring functions based on PEs and propose the corresponding models for TVMI problem solving by using the substitution technique and ZNN design formula. In order to facilitate computer simulation, the obtained continuous-time models are discretized by using ZTD (Zhang time discretization) formulas. Furthermore, the feasibility and effectiveness of the novel Zhang neural network (ZNN) multiple-multiplication model for matrix inverse (ZMMMI) and the PEs-based Getz–Marsden dynamic system (PGMDS) model in solving the problem of TVMI are investigated and shown via theoretical derivation and computer simulation. Computer experiment results also illustrate that the direct derivative dynamics model for TVMI is less effective and feasible.Dongqing WuYunong ZhangHindawi LimitedarticleMathematicsQA1-939ENDiscrete Dynamics in Nature and Society, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Dongqing Wu Yunong Zhang From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique
description	The time-variant matrix inversion (TVMI) problem solving is the hotspot of current research because of its frequent appearance and application in scientific research and industrial production. The generalized inverse problem of singular square matrix and nonsquare matrix can be related to Penrose equations (PEs). The PEs implicitly define the generalized inverse of a known matrix, which is of fundamental theoretical significance. Therefore, the in-depth study of PEs might enlighten problem solving of TVMI in a foreseeable way. For the first time, we construct three different matrix error-monitoring functions based on PEs and propose the corresponding models for TVMI problem solving by using the substitution technique and ZNN design formula. In order to facilitate computer simulation, the obtained continuous-time models are discretized by using ZTD (Zhang time discretization) formulas. Furthermore, the feasibility and effectiveness of the novel Zhang neural network (ZNN) multiple-multiplication model for matrix inverse (ZMMMI) and the PEs-based Getz–Marsden dynamic system (PGMDS) model in solving the problem of TVMI are investigated and shown via theoretical derivation and computer simulation. Computer experiment results also illustrate that the direct derivative dynamics model for TVMI is less effective and feasible.
format	article
author	Dongqing Wu Yunong Zhang
author_facet	Dongqing Wu Yunong Zhang
author_sort	Dongqing Wu
title	From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique
title_short	From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique
title_full	From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique
title_fullStr	From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique
title_full_unstemmed	From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique
title_sort	from penrose equations to zhang neural network, getz–marsden dynamic system, and ddd (direct derivative dynamics) using substitution technique
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/cb87b135b2604947a4064b98ed7ff6f1
work_keys_str_mv	AT dongqingwu frompenroseequationstozhangneuralnetworkgetzmarsdendynamicsystemandddddirectderivativedynamicsusingsubstitutiontechnique AT yunongzhang frompenroseequationstozhangneuralnetworkgetzmarsdendynamicsystemandddddirectderivativedynamicsusingsubstitutiontechnique
_version_	1718407734839214080

From Penrose Equations to Zhang Neural Network, Getz–Marsden Dynamic System, and DDD (Direct Derivative Dynamics) Using Substitution Technique

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