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Tr. Mat. Inst. Steklova, 2010, Volume 270, Pages 281–287 (Mi tm3020)  

This article is cited in 4 scientific papers (total in 4 papers)

On a nontraditional method of approximation

P. V. Chunaev

Chair of Functional Analysis and Its Applications, Vladimir State University, Vladimir, Russia

Abstract: We study the approximation of functions $f(z)$ that are analytic in a neighborhood of zero by finite sums of the form $H_n(z)=H_n(h,f,\{\lambda_k\};z)=\sum_{k=1}^n\lambda_kh(\lambda_kz)$, where $h$ is a fixed function that is analytic in the unit disk $|z|<1$ and the numbers $\lambda_k$ (which depend on $h,f$, and $n$) are calculated by a certain algorithm. An exact value of the radius of the convergence $H_n(z)\to f(z)$, $n\to\infty$, and an order-sharp estimate for the rate of this convergence are obtained; an application to numerical analysis is given.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 270, 278–284

Bibliographic databases:

UDC: 517.538.5
Received in January 2010

Citation: P. V. Chunaev, “On a nontraditional method of approximation”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 281–287; Proc. Steklov Inst. Math., 270 (2010), 278–284

Citation in format AMSBIB
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\paper On a~nontraditional method of approximation
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
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\vol 270
\pages 281--287
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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. P. V. Chunaev, “On the Extrapolation of Analytic Functions by Sums of the Form $\sum_k\lambda_k h(\lambda_k z)$”, Math. Notes, 92:5 (2012), 727–730  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Chunaev P., “Least Deviation of Logarithmic Derivatives of Algebraic Polynomials From Zero”, J. Approx. Theory, 185 (2014), 98–106  crossref  mathscinet  zmath  isi  elib  scopus
    3. Chunaev P., Danchenko V., “Approximation by amplitude and frequency operators”, J. Approx. Theory, 207 (2016), 1–31  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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