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Fundam. Prikl. Mat., 1996, Volume 2, Issue 3, Pages 675–774 (Mi fpm168)  

This article is cited in 5 scientific papers (total in 5 papers)

On the complexity of an approximative realization of functional compacts in some spaces and the existence of functions with given order conditions of their complexity

S. B. Gashkov

M. V. Lomonosov Moscow State University

Abstract: The question of the complexity of an approximative computation of functions from various functional compacts by schemes, consisting of continuous functions realizing elements was investigated. It was proved that almost all functions from many compacts (respectively some Kolmogorov's measure) had asymptotically equal complexity, which was equal to the complexity of the most complicated functions from these compacts. It was proved that in considered compacts there exist the functions, which have $\varepsilon$-approximation complexity asymptotically equal to $L(\varepsilon)$, under some natural restrictions.

Full text: PDF file (3182 kB)

Bibliographic databases:
UDC: 519.7+517.5
Received: 01.06.1995

Citation: S. B. Gashkov, “On the complexity of an approximative realization of functional compacts in some spaces and the existence of functions with given order conditions of their complexity”, Fundam. Prikl. Mat., 2:3 (1996), 675–774

Citation in format AMSBIB
\Bibitem{Gas96}
\by S.~B.~Gashkov
\paper On the complexity of an approximative realization of functional compacts in some spaces and the existence of functions with given order conditions of their complexity
\jour Fundam. Prikl. Mat.
\yr 1996
\vol 2
\issue 3
\pages 675--774
\mathnet{http://mi.mathnet.ru/fpm168}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1815557}
\zmath{https://zbmath.org/?q=an:0912.65125}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Marchenkov, “On superpositions of continuous functions defined on a Baire space”, Math. Notes, 66:5 (1999), 577–584  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. S. Marchenkov, “Impossibility of constructing continuous functions of $(n+1)$ variables from functions of $n$ variables by means of certain continuous operators”, Sb. Math., 192:6 (2001), 863–878  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Marchenkov S.S., “Operatory iterirovaniya na mnozhestve nepreryvnykh funktsii berovskogo prostranstva”, Vestnik Moskovskogo universiteta. Seriya 15: Vychislitelnaya matematika i kibernetika, 4 (2011), 33–37  mathscinet  zmath  elib
    4. Ya. V. Vegner, S. B. Gashkov, “Complexity of Approximate Realizations of Lipschitz Functions by Schemes in Continuous Bases”, Math. Notes, 92:1 (2012), 23–38  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. S. S. Marchenkov, “Interpolation and Superpositions of Multivariate Continuous Functions”, Math. Notes, 93:4 (2013), 571–577  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Фундаментальная и прикладная математика
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