The Activity of K. I. Oskolkov in Nonlinear Approximation of Functions

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 25)


The paper represents the review of activity of K.I. Oskolkov in nonlinear approximation of functions and optimal distribution of quadratures.


Plane Wave Harmonic Function Greedy Algorithm Function Class Radial Function 
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  1. 1.
    DeVore, R.A., Oskolkov, K.I., Petrushev, P.P.: Approximation by feed-forward neural networks. Ann. Numer. Math. 4, 261–287 (1997), The heritage of P.L. Chebyshev: A Festschrift in honor of the 70th birthday of T.J. Rivlin. MR 97i:41043Google Scholar
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    Maiorov, V.E., Oskolkov, K.I., and Temlyakov, V.N.: Gridge approximation and Radon compass. In: Bojanov, B. (ed.) Approximation Theory: A Volume-Dedicated to Blagovest Sendov, pp. 284–309. DARBA, Sofia (2002)Google Scholar
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    Oskolkov, K.I.: On optimality of quadrature formula with uniform knots on classes of periodical functios. Dokl. AN SSSR 249(1), 49–51 (1979)MathSciNetGoogle Scholar
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    Oskolkov, K.I.: On optimal quadrature formula on certain classes of periodic functions. Appl. Math. Optim. 8, 245–263 (1982)MathSciNetMATHCrossRefGoogle Scholar
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    Oskolkov, K.I.: Ridge approximation, Fourier-Chebyshev analysis, and optimal quadrature formulas. Tr. Mat. Inst. Steklov 219, 269–285 (1997), MR 99j:41036 (Russian)Google Scholar
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    Oskolkov, K.I.: Linear and nonlinear methods for ridge approximation, Metric theory of functions and related problems in analysis (Russian), Izd. Nauchno-Issled. Aktuarno-Finans. Tsentra (AFTs), Moscow, 165–195 (1999) MR 2001i:41039 (Russian, with Russian summary)Google Scholar
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    Oskolkov, K.I.: Ridge approximation and the Kolmogorov-Nikolskii problem. Dokl. Akad. Nauk 368, 445–448 (1999), MR 2001b:41024 (Russian)Google Scholar
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    Oskolkov, K.I.: On representations of algebraic polynomials by superpositions of plane waves. Serdica Math. J. 28, 379–390 (2002), Dedicated to the memory of Vassil Popov on the occasion of his 60th birthdayGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsTechnionHaifaIsrael

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