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Doklady Akademii Nauk SSSR, 1957, Volume 114, Number 5, Pages 953–956 (Mi dan22050)  

This article is cited in 43 scientific papers (total in 44 papers)

MATHEMATICS

On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition

A. N. Kolmogorov
Received: 20.06.1957
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. N. Kolmogorov, “On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition”, Dokl. Akad. Nauk SSSR, 114:5 (1957), 953–956
Citation in format AMSBIB
\Bibitem{Kol57}
\by A.~N.~Kolmogorov
\paper On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition
\jour Dokl. Akad. Nauk SSSR
\yr 1957
\vol 114
\issue 5
\pages 953--956
\mathnet{http://mi.mathnet.ru/dan22050}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=0111809}
\zmath{https://zbmath.org/?q=an:0090.27103}
Linking options:
  • https://www.mathnet.ru/eng/dan22050
  • https://www.mathnet.ru/eng/dan/v114/i5/p953
  • This publication is cited in the following 44 articles:
    1. P. V. Kuptsov, N. V. Stankevich, “Modelirovanie dinamiki neironnykh ostsillyatorov tipa Khodzhkina-Khaksli pri pomoschi neironnoi seti”, Izvestiya vuzov. PND, 32:1 (2024), 72–95  mathnet  crossref
    2. O. E. Kudryavtsev, A. S. Grechko, I. E. Mamadov, “Monte Carlo method for pricing lookback options in Lévy models”, Theory Probab. Appl., 69:2 (2024), 243–264  mathnet  crossref  crossref
    3. V. K. Beloshapka, “Geometric constructions in the theory of analytic complexity”, Izv. Math., 88:3 (2024), 411–418  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. N. F. Aleksiadis, “Analog teoremy Kolmogorova o superpozitsiyakh nepreryvnykh funktsii dlya funktsionalnykh sistem polinomialnykh i ratsionalnykh funktsii”, Chebyshevskii sb., 25:2 (2024), 29–42  mathnet  crossref
    5. M. H. Dao, F. Liu, D. N. Sidorov, “Kolmogorov–Arnold neural networks technique for the state of charge estimation for Li-ion batteries”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 17:4 (2024), 22–31  mathnet  crossref
    6. A. D. Smorodinov, T. V. Gavrilenko, V. A. Galkin, “Primenimost geneticheskikh algoritmov dlya opredeleniya vesovykh koeffitsientov iskusstvennoi neironnoi seti s odnim skrytym sloem”, Vestnik KRAUNTs. Fiz.-mat. nauki, 43:2 (2023), 69–86  mathnet  crossref
    7. A. D. Smorodinov, T. V. Gavrilenko, V. A. Galkin, “Teoreticheskie osnovy iskusstvennykh neironnykh setei dlya resheniya zadachi approksimatsii i interpolyatsii”, Uspekhi kibernetiki, 4:4 (2023), 41–53  mathnet  crossref
    8. I. V. Boikov, “Nauchnye issledovaniya na kafedre «Vysshaya i prikladnaya matematika» Penzenskogo gosudarstvennogo universiteta (1943-2023)”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2023, no. 4, 189–216  mathnet  crossref
    9. V. A. Galkin, T. V. Gavrilenko, A. D. Smorodinov, “Nekotorye aspekty approksimatsii i interpolyatsii funktsii iskusstvennymi neironnymi setyami”, Vestnik KRAUNTs. Fiz.-mat. nauki, 38:1 (2022), 54–73  mathnet  crossref  mathscinet
    10. Yu. S. Kharin, V. A. Voloshko, “On the approximation of high-order binary Markov chains by parsimonious models”, Discrete Math. Appl., 34:2 (2024), 71–87  mathnet  crossref  crossref
    11. M. A. Stepanova, “O funktsiyakh konechnoi analiticheskoi slozhnosti”, Tr. MMO, 83, no. 1, MTsNMO, M., 2022, 1–16  mathnet
    12. V. G. Shishlyakov, “O postroenii yavnoi arkhitektury neironnoi seti, priblizhayuschei kusochno-lineinye funktsii”, Intellektualnye sistemy. Teoriya i prilozheniya, 26:2 (2022), 42–60  mathnet
    13. P. V. Kuptsov, A. V. Kuptsova, N. V. Stankevich, “Artificial Neural Network as a Universal Model of Nonlinear Dynamical Systems”, Rus. J. Nonlin. Dyn., 17:1 (2021), 5–21  mathnet  crossref  mathscinet
    14. N. A. Vershkov, M. G. Babenko, V. A. Kuchukov, N. N. Kuchukova, “Obuchenie mnogosloinogo pertseptrona s uchitelem v zadache raspoznavaniya s pomoschyu korrelyatsionnogo pokazatelya”, Trudy ISP RAN, 33:1 (2021), 33–46  mathnet  crossref
    15. A. D. Obukhov, M. N. Krasnyanskii, “Neirosetevoi metod obrabotki i peredachi dannykh v adaptivnykh informatsionnykh sistemakh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:1 (2021), 149–164  mathnet  crossref
    16. A. V. Chernov, “Gaussian functions combined with Kolmogorov's theorem as applied to approximation of functions of several variables”, Comput. Math. Math. Phys., 60:5 (2020), 766–782  mathnet  crossref  crossref  isi  elib
    17. N. A. Vershkov, V. A. Kuchukov, N. N. Kuchukova, “Teoreticheskii podkhod k poisku globalnogo ekstremuma pri obuchenii neironnykh setei”, Trudy ISP RAN, 31:2 (2019), 41–52  mathnet  crossref  elib
    18. A. S. Shvedov, “Approksimatsiya funktsii s pomoschyu neironnykh setei i nechetkikh sistem”, Probl. upravl., 1 (2018), 21–29  mathnet
    19. S. V. Konyagin, A. A. Kuleshov, V. E. Maiorov, “Some problems in the theory of ridge functions”, Proc. Steklov Inst. Math., 301 (2018), 144–169  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    20. A. I. Ivanov, P. S. Lozhnikov, A. E. Sulavko, “Otsenka nadezhnosti verifikatsii avtografa na osnove iskusstvennykh neironnykh setei, setei mnogomernykh funktsionalov Baiesa i setei kvadratichnykh form”, Kompyuternaya optika, 41:5 (2017), 765–774  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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