Chinese Journal of Computers   Full Text
Title	Serial Function Networks Method and Learning Algorithm with Applications
Authors	ZHOU Yong-Quan1),2) ZHAO Bin3) JIAO Li-Cheng1)
Address	1)(Institute for Intelligence Information Processing, Xidian University, Xi’an 710071) 2)(College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006) 3)(School of Science, Central University for Nationalities, Beijing 100081)
Year	2008
Issue	No.7(1073—1081)
Abstract &   Background	Abstract In this paper, by analyzing the functional network, a new model and learning algorithm of the serial functional networks is proposed. And the learning of parameters of the serial functional networks is carried out by the gradient descent algorithm. Based on this, nine kinds of serial function networks for solving classical functional equations and a kind of solving functional equations method on serial functional networks are presented. The simulation results show that the identification method presented in the paper has rapid convergence speed and powerful performance. Contrary to traditional numerical method, this method in this paper could be used to solve arbitrary functional equations. Keywords functional network; serial functional network; learning algorithm; functional equations Background This work is supported by the National Natural Science Foundation of China under grant No.60461001 and the Natural Science Foundation of Guangxi under grant No.0542048. Functional network is new network model. It is similar to artificial neural network and is network expression of functional equation. The authors have made a lot of researches on the development of functional network and proposed some new functional network models and learning algorithms which have been applied to the computer algebra. In this paper, based on serial functional networks, a learning algorithm of the serial functional networks is proposed. And the learning of parameters of the serial functional networks is carried out by the gradient descent algorithm. Based on this, nine kinds of serial function networks for solving some important functional equations and a kind of solving functional equations method on serial functional networks are presented. The simulation results demonstrate that the identification method presented in the paper has rapid convergence speed and powerful performance. Contrary to traditional numerical method, this method in this paper could be used to solve general functional equations.