A~generalized approximation theorem and an exact representation of polynomials of several variables by superpositions of polynomials of one variable
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (1998), pp. 6-9.

Voir la notice de l'article provenant de la source Math-Net.Ru

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A. N. Gorban'. A~generalized approximation theorem and an exact representation of polynomials of several variables by superpositions of polynomials of one variable. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (1998), pp. 6-9. http://geodesic.mathdoc.fr/item/IVM_1998_5_a1/

[1] Kolmogorov A. N., “O predstavlenii nepreryvnykh funktsii neskolkikh peremennykh superpozitsiyami nepreryvnykh funktsii menshego chisla peremennykh”, DAN SSSR, 108:2 (1956), 179–182 | MR

[2] Arnold V. I., “O funktsiyakh trekh peremennykh”, DAN SSSR, 114:4 (1957), 679–681 | MR

[3] Kolmogorov A. N., “O predstavlenii nepreryvnykh funktsii neskolkikh peremennykh v vide superpozitsii nepreryvnykh funktsii odnogo peremennogo i slozheniya”, DAN SSSR, 114:5 (1957), 953–956 | MR

[4] Gorban A. N., Obuchenie neironnykh setei, Izd. SSSR-SShA SP “ParaGraf”, M., 1990, 160 pp.

[5] Zurada J. M., Introduction to artificial neural systems, PWS Publishing Company, New York, 1992, 785 pp.

[6] Stone M. N., “The generalized Weierstrass approximation theorem”, Math. Mag., 21 (1948), 167–183 | MR

[7] Gorban A. N., Rossiev D. A., Neironnye seti na personalnom kompyutere, Nauka, Novosibirsk, 1996, 276 pp. | MR

[8] Cybenko G., “Approximation by superposition of a sigmoidal function”, Math. Control, Signals and Systems, 2 (1989), 303–314 | DOI | MR | Zbl

[9] Hornik K., Stinchcombe M., White H., “Multilayer feedforward networks are universal approximators”, Neural Networks, 2 (1989), 359–366 | DOI

[10] Kochenov D. A., Rossiev D. A., “Approximations of functions of $C[A, B]$ class by neural-net predictors (architectures and results)”, Neurocomputing, AMSE Transaction, Scientific Siberian, A, 6, Tassin, France, 1993, 189–203

[11] Gilev S. E., Gorban A. N., “On completness 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), Lawrens Erlbaum Accociates, 1996, 984–991