General Recurrent Neural Network for Solving Generalized Linear Matrix Equation

This brief proposes a general framework of the nonlinear recurrent neural network for solving online the generalized linear matrix equation (GLME) with global convergence property. If the linear activation function is utilized, the neural state matrix of the nonlinear recurrent neural network can gl...

Full description

Saved in:
Bibliographic Details
Main Authors: Zhan Li, Hong Cheng, Hongliang Guo
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2017/9063762
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832559083661557760
author Zhan Li
Hong Cheng
Hongliang Guo
author_facet Zhan Li
Hong Cheng
Hongliang Guo
author_sort Zhan Li
collection DOAJ
description This brief proposes a general framework of the nonlinear recurrent neural network for solving online the generalized linear matrix equation (GLME) with global convergence property. If the linear activation function is utilized, the neural state matrix of the nonlinear recurrent neural network can globally and exponentially converge to the unique theoretical solution of GLME. Additionally, as compared with the case of using the linear activation function, two specific types of nonlinear activation functions are proposed for the general nonlinear recurrent neural network model to achieve superior convergence. Illustrative examples are shown to demonstrate the efficacy of the general nonlinear recurrent neural network model and its superior convergence when activated by the aforementioned nonlinear activation functions.
format Article
id doaj-art-81ffe6f8204b4d0f9ff7b85133bf3a3a
institution Kabale University
issn 1076-2787
1099-0526
language English
publishDate 2017-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-81ffe6f8204b4d0f9ff7b85133bf3a3a2025-02-03T01:30:54ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/90637629063762General Recurrent Neural Network for Solving Generalized Linear Matrix EquationZhan Li0Hong Cheng1Hongliang Guo2School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, ChinaThis brief proposes a general framework of the nonlinear recurrent neural network for solving online the generalized linear matrix equation (GLME) with global convergence property. If the linear activation function is utilized, the neural state matrix of the nonlinear recurrent neural network can globally and exponentially converge to the unique theoretical solution of GLME. Additionally, as compared with the case of using the linear activation function, two specific types of nonlinear activation functions are proposed for the general nonlinear recurrent neural network model to achieve superior convergence. Illustrative examples are shown to demonstrate the efficacy of the general nonlinear recurrent neural network model and its superior convergence when activated by the aforementioned nonlinear activation functions.http://dx.doi.org/10.1155/2017/9063762
spellingShingle Zhan Li
Hong Cheng
Hongliang Guo
General Recurrent Neural Network for Solving Generalized Linear Matrix Equation
Complexity
title General Recurrent Neural Network for Solving Generalized Linear Matrix Equation
title_full General Recurrent Neural Network for Solving Generalized Linear Matrix Equation
title_fullStr General Recurrent Neural Network for Solving Generalized Linear Matrix Equation
title_full_unstemmed General Recurrent Neural Network for Solving Generalized Linear Matrix Equation
title_short General Recurrent Neural Network for Solving Generalized Linear Matrix Equation
title_sort general recurrent neural network for solving generalized linear matrix equation
url http://dx.doi.org/10.1155/2017/9063762
work_keys_str_mv AT zhanli generalrecurrentneuralnetworkforsolvinggeneralizedlinearmatrixequation
AT hongcheng generalrecurrentneuralnetworkforsolvinggeneralizedlinearmatrixequation
AT hongliangguo generalrecurrentneuralnetworkforsolvinggeneralizedlinearmatrixequation