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...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/9063762 |
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| _version_ | 1832559083661557760 |
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| 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 |