Approximation of polynomial functions by neural network: Construction of network and algorithm of approximation

Jisuanji Xuebao/Chinese Journal of Computers

Volumn 26, Issue 8, 2003, Pages 906-912

  Cao, Fei Long ^a   Xu, Zong Ben ^b   Liang, Ji Ye ^c  

^a SHAOXING COLLEGE OF ARTS AND SCIENCES   (China)

^b XI'AN JIAOTONG UNIVERSITY   (China)

^c SHANXI UNIVERSITY   (China)

Author keywords

Algorithm; Approximation; Feed forward neural network; Polynomial function

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FUNCTIONS; MULTILAYER NEURAL NETWORKS; POLYNOMIALS; THEOREM PROVING;

APPROXIMATION ALGORITHMS; CONSTRUCTIVE METHOD; NETWORK CONSTRUCTION; POLYNOMIAL FUNCTIONS; THREE LAYER NEURAL NETWORKS;

FEEDFORWARD NEURAL NETWORKS;

EID: 0344036321     PISSN: 02544164     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

1. Cybenko G. Approximation by superpositions of sigmoidal function. Math of Control, Signals, and System, 1989, 2(4): 303-314.
2. Funahashi K. On the approximate realization of continuous mappings by neural networks. Neural Networks, 1989, 2(1): 183-192.
3. Hornik K, Stinchombe M, White H. Multilayer feedforward networks are universal approximators. Neural Networks, 1989, 2(2): 359-366.
4. Leshno M, Lin V Y, Pinks A, Schocken S. Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Networks, 1993, 6(5): 861-867.
5. Chen Tian-Ping. Neural network and its approximation problems in system identification. Science in China (Series A), 1994, 24(1): 1-7 (in Chinese)
6. Kurkova V, Kainen P C, Kreinovich V. Estimates of the number of hidden units and variation with respect to half-space. Neural Networks, 1997, 10(6): 1068-1078.
7. Suzuki Shin. Constructive function approximation by three-layer artificial neural networks. Neural Networks, 1998, 11(6): 1049-1058.
8. d) by neural and mixture networks. IEEE Transactions on Neural Networks, 1998, 9(5): 969-978.
9. Chen X H, White H. Improve rates and asymptotic normality for nonparametric neural network estimators. IEEE Transactions on Information Theory, 1999, 45(4): 682-691.
10. Cao F L, Xu Z B. Neural network approximation for multivariate periodic functions: Estimates of approximation order. Chinese Journal of Computer, 2001, 24(9): 903-908 (in Chinese)
11. Attali J G, Pages G. Approximation of functions by a multilayer perception: A new approach. Neural Networks, 1997, 10(6): 1069-1081.