메뉴 건너뛰기




Volumn 58, Issue 4, 2009, Pages 758-765

The approximation operators with sigmoidal functions

Author keywords

Approximation; Error estimates; Neural networks; Quasi interpolation; Sigmoidal function

Indexed keywords

APPROXIMATION; APPROXIMATION OPERATORS; CONTINUOUS FUNCTIONS; ERROR ESTIMATES; QUASI-INTERPOLATION; SIGMOIDAL FUNCTION; SIGMOIDAL FUNCTIONS; UNIFORM NORM; UPPER BOUND;

EID: 67649743440     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.05.001     Document Type: Article
Times cited : (200)

References (23)
  • 3
    • 0024861871 scopus 로고
    • Approximation by superpositions of sigmoidal function
    • Cybenko G. Approximation by superpositions of sigmoidal function. Math. of Control Signals, and System 2 (1989) 303-314
    • (1989) Math. of Control Signals, and System , vol.2 , pp. 303-314
    • Cybenko, G.1
  • 4
    • 0024866495 scopus 로고
    • On the approximate realization of continuous mappings by neural networks
    • Funahashi K.I. On the approximate realization of continuous mappings by neural networks. Neural Netw. 2 (1989) 183-192
    • (1989) Neural Netw. , vol.2 , pp. 183-192
    • Funahashi, K.I.1
  • 5
    • 0024880831 scopus 로고
    • Multilayer feedforward networks are universal approximation
    • Hornik K., Stinchcombe M., and White H. Multilayer feedforward networks are universal approximation. Neural Netw. 2 (1989) 359-366
    • (1989) Neural Netw. , vol.2 , pp. 359-366
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 6
    • 0025627940 scopus 로고
    • Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
    • Hornik K., Stinchcombe M., and White H. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Netw. 3 (1990) 551-560
    • (1990) Neural Netw. , vol.3 , pp. 551-560
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 7
    • 0027262895 scopus 로고
    • Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
    • Leshno M., Lin V.Y., Pinks A., and Schocken S. Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Netw. 6 (1993) 861-867
    • (1993) Neural Netw. , vol.6 , pp. 861-867
    • Leshno, M.1    Lin, V.Y.2    Pinks, A.3    Schocken, S.4
  • 8
    • 0000358945 scopus 로고
    • Approximation by superposition of a sigmoidal function
    • Mhaskar H.N., and Micchelli C.A. Approximation by superposition of a sigmoidal function. Adv. Appl. Math. 13 (1992) 350-373
    • (1992) Adv. Appl. Math. , vol.13 , pp. 350-373
    • Mhaskar, H.N.1    Micchelli, C.A.2
  • 9
    • 0000378922 scopus 로고
    • Approximation by ridge functions and neural networks with one hidden layer
    • Chui C.K., and Li X. Approximation by ridge functions and neural networks with one hidden layer. J. Approx. Theory 70 (1992) 131-141
    • (1992) J. Approx. Theory , vol.70 , pp. 131-141
    • Chui, C.K.1    Li, X.2
  • 10
    • 0029343809 scopus 로고
    • Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to a dynamic system
    • Chen T.P., and Chen H. Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to a dynamic system. IEEE Trans. Neural Netw. 6 (1995) 911-917
    • (1995) IEEE Trans. Neural Netw. , vol.6 , pp. 911-917
    • Chen, T.P.1    Chen, H.2
  • 11
    • 9644287964 scopus 로고    scopus 로고
    • An approximation by neural networks with a fixed weight
    • Hahm N., and Hong B.I. An approximation by neural networks with a fixed weight. Comput. & Math. Appl. 47 (2004) 1897-1903
    • (2004) Comput. & Math. Appl. , vol.47 , pp. 1897-1903
    • Hahm, N.1    Hong, B.I.2
  • 12
    • 0027599793 scopus 로고
    • Universal approximation bounds for superpositions of a sigmoidal function
    • Barron A.R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39 (1993) 930-945
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 13
    • 0000194429 scopus 로고
    • Degree of approximation by neural networks with a single hidden layer
    • Mhaskar H.N., and Miccheli C.A. Degree of approximation by neural networks with a single hidden layer. Adv. Appl. Math. 16 (1995) 151-183
    • (1995) Adv. Appl. Math. , vol.16 , pp. 151-183
    • Mhaskar, H.N.1    Miccheli, C.A.2
  • 14
    • 0032144406 scopus 로고    scopus 로고
    • Constructive function approximation by three-layer artificial neural networks
    • Suzuki S. Constructive function approximation by three-layer artificial neural networks. Neural Netw. 11 (1998) 1049-1058
    • (1998) Neural Netw. , vol.11 , pp. 1049-1058
    • Suzuki, S.1
  • 16
    • 0001574595 scopus 로고    scopus 로고
    • Uniform approximation by neural networks
    • Makovoz Y. Uniform approximation by neural networks. J. Approx. Theory 95 (1998) 215-228
    • (1998) J. Approx. Theory , vol.95 , pp. 215-228
    • Makovoz, Y.1
  • 17
    • 13844255524 scopus 로고    scopus 로고
    • Smooth function approximation using neural networks
    • Ferrari S., and Stengel R.F. Smooth function approximation using neural networks. IEEE Trans. Neural Networks 16 (2005) 24-38
    • (2005) IEEE Trans. Neural Networks , vol.16 , pp. 24-38
    • Ferrari, S.1    Stengel, R.F.2
  • 18
    • 24344496437 scopus 로고    scopus 로고
    • The essential order of approximation for neural networks
    • Xu Z.B., and Cao F.L. The essential order of approximation for neural networks. Sci. China Ser. F 47 (2004) 97-112
    • (2004) Sci. China Ser. F , vol.47 , pp. 97-112
    • Xu, Z.B.1    Cao, F.L.2
  • 19
    • 0031195377 scopus 로고    scopus 로고
    • Rate of convergence of some neural network operators to the unit-univariate case
    • Anastassiou G.A. Rate of convergence of some neural network operators to the unit-univariate case. J. Math. Anal. Appl. 212 (1997) 237-262
    • (1997) J. Math. Anal. Appl. , vol.212 , pp. 237-262
    • Anastassiou, G.A.1
  • 20
    • 38649094938 scopus 로고    scopus 로고
    • The estimate for approximation error of neural networks: A constructive approach
    • Cao F.L., Xie T.F., and Xu Z.B. The estimate for approximation error of neural networks: A constructive approach. Neurocomputing 71 (2008) 626-630
    • (2008) Neurocomputing , vol.71 , pp. 626-630
    • Cao, F.L.1    Xie, T.F.2    Xu, Z.B.3
  • 23
    • 84953751498 scopus 로고
    • Cambridge University Press, Cambridge
    • Zygmund A. Trigonometric Series (1959), Cambridge University Press, Cambridge
    • (1959) Trigonometric Series
    • Zygmund, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.