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Volumn 11, Issue 3, 1998, Pages 45-49

Approximation of continuous functions of several variables by an arbitrary nonlinear continuous function of one variable, linear functions, and their superpositions

(1)  Gorban', A N a  

a NONE

Author keywords

Approximation; Neural networks; Superposition; Weierstrass theorem

Indexed keywords


EID: 0002271590     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(98)00032-9     Document Type: Article
Times cited : (41)

References (13)
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  • 2
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    • On representation of continuous functions of several variables by superpositions of continuous functions of smaller number of variables
    • A.N. Kolmogorov, On representation of continuous functions of several variables by superpositions of continuous functions of smaller number of variables, Dokl. AN SSSR 108 (2), 179-182 (1956).
    • (1956) Dokl. AN SSSR , vol.108 , Issue.2 , pp. 179-182
    • Kolmogorov, A.N.1
  • 3
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    • On the functions of three variables
    • V.I. Arnold, On the functions of three variables, Dokl. AN SSSR 114 (4), 679-681 (1957).
    • (1957) Dokl. AN SSSR , vol.114 , Issue.4 , pp. 679-681
    • Arnold, V.I.1
  • 4
    • 0001321136 scopus 로고
    • On representation of continuous functions of several variables as superpositions of continuous functions of one variable
    • A.N. Kolmogorov, On representation of continuous functions of several variables as superpositions of continuous functions of one variable, Dokl. AN SSSR 114 (5), 953-956 (1957).
    • (1957) Dokl. AN SSSR , vol.114 , Issue.5 , pp. 953-956
    • Kolmogorov, A.N.1
  • 6
    • 0040818406 scopus 로고
    • USSR-USA JV "ParaGraph", Moscow
    • A.N. Gorban, Training Neural Networks, USSR-USA JV "ParaGraph", Moscow, (1990); English translation, AMSE Transaction, Scientific Siberian, A, Volume 6, Neurocomputing, pp. 1-134, Tassin, France, (1993).
    • (1990) Training Neural Networks
    • Gorban, A.N.1
  • 7
    • 0043278093 scopus 로고
    • English translation, Neurocomputing, Tassin, France
    • A.N. Gorban, Training Neural Networks, USSR-USA JV "ParaGraph", Moscow, (1990); English translation, AMSE Transaction, Scientific Siberian, A, Volume 6, Neurocomputing, pp. 1-134, Tassin, France, (1993).
    • (1993) AMSE Transaction, Scientific Siberian, A , vol.6 , pp. 1-134
  • 9
    • 0024861871 scopus 로고
    • Approximation by superposition of a sigmoidal function
    • G. Cybenko, Approximation by superposition of a sigmoidal function, Mathematics of Control, Signals, and Systems 2, 303-314 (1989).
    • (1989) Mathematics of Control, Signals, and Systems , vol.2 , pp. 303-314
    • Cybenko, G.1
  • 10
    • 0024880831 scopus 로고
    • Multilayer feedforward networks are universal approximators
    • K. Hornik, M. Stinchcombe and H. White, Multilayer feedforward networks are universal approximators, Neural Networks 2, 359-366 (1989).
    • (1989) Neural Networks , vol.2 , pp. 359-366
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 11
    • 0039907457 scopus 로고
    • Approximations of functions of C[A, B] class by neural-net predictors (architectures and results)
    • Neurocomputing, Tassin, France
    • D.A. Kochenov and D.A. Rossiev, Approximations of functions of C[A, B] class by neural-net predictors (architectures and results), AMSE Transaction, Scientific Siberian, A, Volume 6, Neurocomputing, pp. 189-203, Tassin, France, (1993).
    • (1993) AMSE Transaction, Scientific Siberian, A , vol.6 , pp. 189-203
    • Kochenov, D.A.1    Rossiev, D.A.2
  • 12
    • 0026118869 scopus 로고
    • On the computation efficiency of symmetric neural networks
    • J. Wiedermann, On the computation efficiency of symmetric neural networks, Theor. Comput. Sci. 80 (2), 337-345 (1991).
    • (1991) Theor. Comput. Sci. , vol.80 , Issue.2 , pp. 337-345
    • Wiedermann, J.1
  • 13
    • 0039418398 scopus 로고    scopus 로고
    • On completeness of the class of functions computable by neural networks
    • Sept. 15-18, 1996, San Diego, CA, Lawrens Erlbaum Accociates
    • S.E. Gilev and A.N. Gorban, On completeness of the class of functions computable by neural networks, Proc. of the World Congress on Neural Networks (WCNN'96), Sept. 15-18, 1996, San Diego, CA, pp. 984-991, Lawrens Erlbaum Accociates, (1996).
    • (1996) Proc. of the World Congress on Neural Networks (WCNN'96) , pp. 984-991
    • Gilev, S.E.1    Gorban, A.N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.