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Mat. Zametki, 2008, Volume 84, Issue 6, Pages 882–887 (Mi mz4168)  

This article is cited in 2 scientific papers (total in 2 papers)

Best Local Approximation by Simplest Fractions

Ya. V. Novak

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: In this paper, we present two theorems on best local approximation by simplest fractions, i.e., by logarithmic derivatives of algebraic polynomials with complex coefficients. In Theorem 1, we obtain an analog of Bernstein's well-known theorem on the description of $n$-times continuously differentiable functions on the closed interval $\Delta\subset\mathbb R$ in terms of local approximations in the uniform metric by algebraic polynomials. Theorem 2 describes the simplest Padé fraction as the limit of the sequence of simplest fractions of best uniform approximation and is an analog of Walsh's well-known result on the classical Padé fractions.

Keywords: best local approximation by simplest fractions, algebraic polynomial, Walsh's theorem, Padé simplest fraction

DOI: https://doi.org/10.4213/mzm4168

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English version:
Mathematical Notes, 2008, 84:6, 821–825

Bibliographic databases:

UDC: 517.538.5
Received: 23.10.2007

Citation: Ya. V. Novak, “Best Local Approximation by Simplest Fractions”, Mat. Zametki, 84:6 (2008), 882–887; Math. Notes, 84:6 (2008), 821–825

Citation in format AMSBIB
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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. A. Borodin, “Approximation by simple partial fractions on the semi-axis”, Sb. Math., 200:8 (2009), 1127–1148  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
  • Математические заметки Mathematical Notes
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