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

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.

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Bibliographic databases:
UDC: 519.7+517.5

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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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
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
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
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
5. S. S. Marchenkov, “Interpolation and Superpositions of Multivariate Continuous Functions”, Math. Notes, 93:4 (2013), 571–577
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