메뉴 건너뛰기




Volumn 14, Issue 1, 2012, Pages 101-112

The construction and approximation of a class of neural networks operators with ramp functions

Author keywords

Modulus of continuity; Neural network operators; Order of approximation

Indexed keywords


EID: 84863018410     PISSN: 15211398     EISSN: 15729206     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (43)

References (18)
  • 1
    • 0031195377 scopus 로고    scopus 로고
    • Rate of convergence of some neural network operators to the unitunivariate case
    • G. A. Anastassiou, Rate of convergence of some neural network operators to the unitunivariate case, J. Math. Anal. Appli., 212 (1997), 237-262.
    • (1997) J. Math. Anal. Appli. , vol.212 , pp. 237-262
    • Anastassiou, G.A.1
  • 2
    • 0034231016 scopus 로고    scopus 로고
    • Rate of convergence of some multivaiate neural network operators to the unit
    • G. A. Anastassiou, Rate of convergence of some multivaiate neural network operators to the unit, Computers and Mathematics with Applications, 40 (2000), 1-19.
    • (2000) Computers and Mathematics with Applications , vol.40 , pp. 1-19
    • Anastassiou, G.A.1
  • 4
    • 84863038500 scopus 로고    scopus 로고
    • Substantial approximation order for neural networks
    • F. L. Cao and Z. B. Xu, Substantial approximation order for neural networks, Science in China, Series A, 34 (2004), 65-74.
    • (2004) Science in China, Series A , vol.34 , pp. 65-74
    • Cao, F.L.1    Xu, Z.B.2
  • 5
    • 0026727494 scopus 로고
    • Approximation of a function and its derivative with a neural network
    • P. Cardaliaguet and G. Euvrard, Approximation of a function and its derivative with a neural network, Neural Networks, 5 (1992), 207-220.
    • (1992) Neural Networks , vol.5 , pp. 207-220
    • Cardaliaguet, P.1    Euvrard, G.2
  • 6
    • 77953536452 scopus 로고    scopus 로고
    • Approximation with neural networks activated by ramp sigmoids
    • H. L. Cheang Gerald, Approximation with neural networks activated by ramp sigmoids, J. Approx. Theory, 162 (2010), 1450-1465.
    • (2010) J. Approx. Theory , vol.162 , pp. 1450-1465
    • Cheang Gerald, H.L.1
  • 7
    • 51249165422 scopus 로고
    • Degree of approximation by superpositions of a sigmoidal function
    • D. B. Chen, Degree of approximation by superpositions of a sigmoidal function, Approx. Theory Appl., 9 (1993), 17-28.
    • (1993) Approx. Theory Appl. , vol.9 , pp. 17-28
    • Chen, D.B.1
  • 8
    • 0041485435 scopus 로고
    • Approximation problems in system identification with neural networks, Science in China
    • T. P. Chen, Approximation problems in system identification with neural networks, Science in China, Series A, 24 (1994), 1-7.
    • (1994) Series A , vol.24 , pp. 1-7
    • Chen, T.P.1
  • 10
    • 67649743440 scopus 로고    scopus 로고
    • The approximation operators with sigmoidal functions
    • Z. X. Chen and F. L. Cao, The approximation operators with sigmoidal functions, Com-puters and Math. with Appl., 58 (2009), 758-765.
    • (2009) Com-puters and Math. With Appl , vol.58 , pp. 758-765
    • Chen, Z.X.1    Cao, F.L.2
  • 12
    • 0024861871 scopus 로고
    • Approximation by superpositions of a sigmoidal function, Mathematics of Control
    • G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control, Signals and Systems, 2(1989), 303-314.
    • (1989) Signals and Systems , vol.2 , pp. 303-314
    • Cybenko, G.1
  • 13
    • 0025751820 scopus 로고
    • Approximation capabilities of multilayer feedforward networks
    • K. Hornik, Approximation capabilities of multilayer feedforward networks, Neural Net-works, 4(1991), 251-257.
    • (1991) Neural Net-works , vol.4 , pp. 251-257
    • Hornik, K.1
  • 14
    • 0027812765 scopus 로고
    • Some new results on neural network approximation
    • K. Hornik, Some new results on neural network approximation, Neural Networks, 6 (1993), 1069-1072.
    • (1993) Neural Networks , vol.6 , pp. 1069-1072
    • Hornik, K.1
  • 15
    • 0025503458 scopus 로고
    • Constructive approximation for neural networks by sigmoid functions
    • L. K. Jones, Constructive approximation for neural networks by sigmoid functions, Pro-ceedings of the IEEE, 78(1990), 1586-1589.
    • (1990) Pro-ceedings of the IEEE , vol.78 , pp. 1586-1589
    • Jones, L.K.1
  • 16
    • 0027262895 scopus 로고
    • Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
    • M. Leshno, V. Y. Lin, A. Pinkus and S. Schocken, Multilayer feedforward networks with a nonpolynomial activation function can approximate any function, Neural Networks, 6(1993), 861-867.
    • (1993) Neural Networks , vol.6 , pp. 861-867
    • Leshno, M.1    Lin, V.Y.2    Pinkus, A.3    Schocken, S.4
  • 17
    • 84863075078 scopus 로고
    • Approximation of functions of several variables and imbedding theorems
    • S. M. Nikolskiǐ, Approximation of functions of several variables and imbedding theorems, Springer-Verlag, 1975.
    • (1975) Springer-Verlag
    • Nikolskiǐ, S.M.1
  • 18
    • 24344486886 scopus 로고    scopus 로고
    • p approximation order for neural networks
    • p approximation order for neural networks, Neural Networks, 18 (2005), 914-923.
    • (2005) Neural Networks , vol.18 , pp. 914-923
    • Xu, Z.B.1    Cao, F.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.