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Complexity of approximation of Lipschitz functions. (English. Russian original) Zbl 1304.68073
Mosc. Univ. Math. Bull. 63, No. 4, 162-164 (2008); translation from Vest. Mosk. Univ. Mat. Mekh. 63, No. 4, 49-51 (2008).
Summary: The attainability of the lower bound by order is proved for the complexity of a problem of approximation of Lipschitz functions by diagrams of functional elements in bases consisting of a finite number of Lipschitz functions and a continuum of constants from a bounded set.
MSC:
68Q25 Analysis of algorithms and problem complexity
41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
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References:
[1] S. B. Gashkov, ”On the Complexity of Approximation of Continuous Functions by Circuits and Formulas in Polynomial and Some Other Bases,” Matem. Voprosy Kibern. 5, 144 (1995).
[2] G. Turán and F. Vatan, ”On the Computation of Boolean Functions by Analog Circuit of Bounded Fan-In,” J. Comput. and Syst. Sci. 54(1), 199 (1997). · Zbl 0869.68050
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