메뉴 건너뛰기




Volumn 191, Issue 2, 2007, Pages 429-439

Hermite interpolation by neural networks

Author keywords

Neural networks; Overfitting avoidance strategies; Univariate and multivariate Hermite interpolation

Indexed keywords

INTERPOLATION; MULTIVARIABLE SYSTEMS; PROBLEM SOLVING;

EID: 34548124676     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.02.107     Document Type: Article
Times cited : (6)

References (33)
  • 1
    • 0024861871 scopus 로고
    • Approximation by superpositions of a sigmoidal function
    • Cybenko G. Approximation by superpositions of a sigmoidal function. Math. Control Signals Syst. 2 (1989) 303-314
    • (1989) Math. Control Signals Syst. , vol.2 , pp. 303-314
    • Cybenko, G.1
  • 2
    • 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 Networks 2 (1989) 183-192
    • (1989) Neural Networks , vol.2 , pp. 183-192
    • Funahashi, K.I.1
  • 3
    • 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 Networks 3 (1990) 551-560
    • (1990) Neural Networks , vol.3 , pp. 551-560
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 4
    • 0027262895 scopus 로고
    • Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
    • Leshno M., Lin V.Y., Pinkus A., and Schochen S. 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    Schochen, S.4
  • 5
    • 0026727494 scopus 로고
    • Approximation of a function and its derivative with a neural network
    • Cardaliaguet P., and Euvrard G. 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
    • 0026449851 scopus 로고
    • On learning the derivatives of an unknown mapping with multilayer feedforward networks
    • Gallant A.R., and White H. On learning the derivatives of an unknown mapping with multilayer feedforward networks. Neural Networks 5 (1992) 129-138
    • (1992) Neural Networks , vol.5 , pp. 129-138
    • Gallant, A.R.1    White, H.2
  • 7
    • 0030221938 scopus 로고    scopus 로고
    • Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer
    • Li X. Simultaneous approximations of multivariate functions and their derivatives by neural networks with one hidden layer. Neurocomputing 12 (1996) 327-343
    • (1996) Neurocomputing , vol.12 , pp. 327-343
    • Li, X.1
  • 8
    • 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
  • 9
    • 21344441889 scopus 로고    scopus 로고
    • Nonlinearity creates linear independence
    • Ito Y. Nonlinearity creates linear independence. Adv. Comput. Math. 5 (1996) 189-203
    • (1996) Adv. Comput. Math. , vol.5 , pp. 189-203
    • Ito, Y.1
  • 10
    • 0009625590 scopus 로고    scopus 로고
    • Superposition of linearly independent functions and finite mappings by neural networks
    • Ito Y., and Saito K. Superposition of linearly independent functions and finite mappings by neural networks. Math. Sci. 21 (1996) 27-33
    • (1996) Math. Sci. , vol.21 , pp. 27-33
    • Ito, Y.1    Saito, K.2
  • 11
    • 0042162507 scopus 로고    scopus 로고
    • Independence of unscaled basis functions and finite mappings by neural networks
    • Ito Y. Independence of unscaled basis functions and finite mappings by neural networks. Math. Sci. 26 (2001) 117-126
    • (2001) Math. Sci. , vol.26 , pp. 117-126
    • Ito, Y.1
  • 12
    • 0026904597 scopus 로고
    • Feedforward nets for interpolation and classification
    • Sontag E.D. Feedforward nets for interpolation and classification. J. Comput. Syst. Sci. 45 (1992) 20-48
    • (1992) J. Comput. Syst. Sci. , vol.45 , pp. 20-48
    • Sontag, E.D.1
  • 13
    • 85011438572 scopus 로고    scopus 로고
    • Approximation theory of the MLP model in neural networks
    • Pinkus A. Approximation theory of the MLP model in neural networks. Acta Numer. (1999) 143-195
    • (1999) Acta Numer. , pp. 143-195
    • Pinkus, A.1
  • 14
    • 0025538692 scopus 로고    scopus 로고
    • Y. Shrivastava, S. Dasgupta, Neural networks for exact matching of functions on a discrete domain, in: Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu, 1990, p. 1719.
  • 15
    • 0026190194 scopus 로고
    • A simple method to derive bounds on the size and to train multilayer neural networks
    • Sartori M.A., and Antsaklis P.J. A simple method to derive bounds on the size and to train multilayer neural networks. IEEE Trans. Neural Networks 2-4 (1991) 467-471
    • (1991) IEEE Trans. Neural Networks , vol.2-4 , pp. 467-471
    • Sartori, M.A.1    Antsaklis, P.J.2
  • 16
    • 0031100287 scopus 로고    scopus 로고
    • Capabilities of a four-layered feedforward neural network
    • Tamura S., and Tateishi M. Capabilities of a four-layered feedforward neural network. IEEE Trans. Neural Networks 8-2 (1997) 251-255
    • (1997) IEEE Trans. Neural Networks , vol.8-2 , pp. 251-255
    • Tamura, S.1    Tateishi, M.2
  • 17
    • 0031673055 scopus 로고    scopus 로고
    • Feedforward neural networks with arbitrary bounded nonlinear activation functions
    • Huang G.B., and Babri H.A. Feedforward neural networks with arbitrary bounded nonlinear activation functions. IEEE Trans. Neural Networks 9-1 (1998) 224-229
    • (1998) IEEE Trans. Neural Networks , vol.9-1 , pp. 224-229
    • Huang, G.B.1    Babri, H.A.2
  • 18
    • 28244460747 scopus 로고    scopus 로고
    • Constructive approximate interpolation by neural networks
    • Llanas B., and Sainz F.J. Constructive approximate interpolation by neural networks. J. Comput. Appl. Math. 188 (2006) 283-308
    • (2006) J. Comput. Appl. Math. , vol.188 , pp. 283-308
    • Llanas, B.1    Sainz, F.J.2
  • 19
    • 0036644587 scopus 로고    scopus 로고
    • Interpolation by ridge polynomials and its application in neural networks
    • Li X. Interpolation by ridge polynomials and its application in neural networks. J. Comput. Appl. Math. 144 (2002) 197-209
    • (2002) J. Comput. Appl. Math. , vol.144 , pp. 197-209
    • Li, X.1
  • 21
    • 0031214134 scopus 로고    scopus 로고
    • Approximations of functions by a multilayer perceptron: a new approach
    • Attali J.G., and Pagès G. Approximations of functions by a multilayer perceptron: a new approach. Neural Networks 10 (1997) 1069-1081
    • (1997) Neural Networks , vol.10 , pp. 1069-1081
    • Attali, J.G.1    Pagès, G.2
  • 22
    • 4644369885 scopus 로고
    • Norms and exclusion theorems
    • Bauer F.L., and Fike C.T. Norms and exclusion theorems. Numer. Math. 2 (1960) 137-141
    • (1960) Numer. Math. , vol.2 , pp. 137-141
    • Bauer, F.L.1    Fike, C.T.2
  • 23
    • 0034289836 scopus 로고    scopus 로고
    • On the history of multivariate polynomial interpolation
    • Gasca M., and Sauer T. On the history of multivariate polynomial interpolation. J. Comput. Appl. Math. 122 (2000) 23-35
    • (2000) J. Comput. Appl. Math. , vol.122 , pp. 23-35
    • Gasca, M.1    Sauer, T.2
  • 24
    • 0034289862 scopus 로고    scopus 로고
    • Multivariate Hermite interpolation by algebraic polynomials: a survey
    • Lorentz R.A. Multivariate Hermite interpolation by algebraic polynomials: a survey. J. Comput. Appl. Math. 122 (2000) 167-201
    • (2000) J. Comput. Appl. Math. , vol.122 , pp. 167-201
    • Lorentz, R.A.1
  • 25
    • 34548118933 scopus 로고    scopus 로고
    • H.E. Salzer, G.M. Kimbro, Tables for bivariate osculatory interpolation over a Cartesian grid. Convair Astronautics, 1958.
  • 27
    • 0042230803 scopus 로고    scopus 로고
    • On a class of Hermite interpolation problems
    • Hakopian H.A. On a class of Hermite interpolation problems. Adv. Comput. Math. 12 (2000) 303-309
    • (2000) Adv. Comput. Math. , vol.12 , pp. 303-309
    • Hakopian, H.A.1
  • 28
    • 34548133849 scopus 로고
    • On lattices admitting unique Lagrange interpolations
    • Chung K.C., and Yao T.H. On lattices admitting unique Lagrange interpolations. SIAM J. Numer. Anal. 22 (1977) 107-113
    • (1977) SIAM J. Numer. Anal. , vol.22 , pp. 107-113
    • Chung, K.C.1    Yao, T.H.2
  • 29
    • 0000095933 scopus 로고
    • Construction of lattices for Lagrange interpolation in projective space
    • Lee S.L., and Phillips G.M. Construction of lattices for Lagrange interpolation in projective space. Constr. Approx. 7 (1991) 283-297
    • (1991) Constr. Approx. , vol.7 , pp. 283-297
    • Lee, S.L.1    Phillips, G.M.2
  • 32
    • 0027246977 scopus 로고
    • On the derivatives of the sigmoid
    • Minai A.A., and Williams R.D. On the derivatives of the sigmoid. Neural Networks 6 (1993) 845-853
    • (1993) Neural Networks , vol.6 , pp. 845-853
    • Minai, A.A.1    Williams, R.D.2
  • 33
    • 0000835513 scopus 로고
    • Lower bounds for the condition number of Vandermonde matrices
    • Gaustschi W., and Inglese G. Lower bounds for the condition number of Vandermonde matrices. Numer. Math. 52 (1988) 241-250
    • (1988) Numer. Math. , vol.52 , pp. 241-250
    • Gaustschi, W.1    Inglese, G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.