Estimation of Approximating Rate for Neural Network inLwp Spaces
A class of Soblove type multivariate function is approximated by feedforward network with one hidden layer of sigmoidal units and a linear output. By adopting a set of orthogonal polynomial basis and under certain assumptions for the governing activation functions of the neural network, the upper bo...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/636078 |
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| _version_ | 1832555079146668032 |
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| author | Jian-Jun Wang Chan-Yun Yang Jia Jing |
| author_facet | Jian-Jun Wang Chan-Yun Yang Jia Jing |
| author_sort | Jian-Jun Wang |
| collection | DOAJ |
| description | A class of Soblove type multivariate function is approximated by feedforward network with one hidden layer of sigmoidal units and a linear output. By adopting a set of orthogonal polynomial basis and under certain assumptions for the governing activation functions of the neural network, the upper bound on the degree of approximation can be obtained for the class of Soblove functions. The results obtained are helpful in understanding the approximation capability and topology construction of the sigmoidal neural networks. |
| format | Article |
| id | doaj-art-d89a3342ac57444ca0e2c9f599b084d9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d89a3342ac57444ca0e2c9f599b084d92025-02-03T05:49:44ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/636078636078Estimation of Approximating Rate for Neural Network inLwp SpacesJian-Jun Wang0Chan-Yun Yang1Jia Jing2School of Mathematics & Statistics, Southwest University, Chongqing 400715, ChinaDepartment of Mechanical Engineering, Taipei Chengshih University of Science and Technology, No.2 Xue-Yuan Rd., Beitou, Taipei 112, TaiwanSchool of Mathematics & Statistics, Southwest University, Chongqing 400715, ChinaA class of Soblove type multivariate function is approximated by feedforward network with one hidden layer of sigmoidal units and a linear output. By adopting a set of orthogonal polynomial basis and under certain assumptions for the governing activation functions of the neural network, the upper bound on the degree of approximation can be obtained for the class of Soblove functions. The results obtained are helpful in understanding the approximation capability and topology construction of the sigmoidal neural networks.http://dx.doi.org/10.1155/2012/636078 |
| spellingShingle | Jian-Jun Wang Chan-Yun Yang Jia Jing Estimation of Approximating Rate for Neural Network inLwp Spaces Journal of Applied Mathematics |
| title | Estimation of Approximating Rate for Neural Network inLwp Spaces |
| title_full | Estimation of Approximating Rate for Neural Network inLwp Spaces |
| title_fullStr | Estimation of Approximating Rate for Neural Network inLwp Spaces |
| title_full_unstemmed | Estimation of Approximating Rate for Neural Network inLwp Spaces |
| title_short | Estimation of Approximating Rate for Neural Network inLwp Spaces |
| title_sort | estimation of approximating rate for neural network inlwp spaces |
| url | http://dx.doi.org/10.1155/2012/636078 |
| work_keys_str_mv | AT jianjunwang estimationofapproximatingrateforneuralnetworkinlwpspaces AT chanyunyang estimationofapproximatingrateforneuralnetworkinlwpspaces AT jiajing estimationofapproximatingrateforneuralnetworkinlwpspaces |