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Mat. Zametki, 2013, Volume 93, Issue 2, Pages 209–215 (Mi mz9203)  

This article is cited in 6 scientific papers (total in 6 papers)

A Criterion for the Best Approximation of Constants by Simple Partial Fractions

M. A. Komarov

Vladimir State University

Abstract: The problem of the best uniform approximation of a real constant $c$ by real-valued simple partial fractions $R_n$ on a closed interval of the real axis is considered. For sufficiently small (in absolute value) $c$, $|c|\leq c_n$, it is proved that $R_n$ is a fraction of best approximation if, for the difference $R_n-c$, there exists a Chebyshev alternance of $n+1$ points on a closed interval. A criterion for best approximation in terms of alternance is stated.

Keywords: best uniform approximation of a real constant, best approximation by simple partial fractions, Chebyshev alternance, interpolation.

DOI: https://doi.org/10.4213/mzm9203

Full text: PDF file (470 kB)
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English version:
Mathematical Notes, 2013, 93:2, 250–256

Bibliographic databases:

UDC: 517.538
Received: 04.07.2011
Revised: 09.11.2011

Citation: M. A. Komarov, “A Criterion for the Best Approximation of Constants by Simple Partial Fractions”, Mat. Zametki, 93:2 (2013), 209–215; Math. Notes, 93:2 (2013), 250–256

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. Chunaev, “Least deviation of logarithmic derivatives of algebraic polynomials from zero”, J. Approx. Theory, 185 (2014), 98–106  crossref  mathscinet  zmath  isi
    2. M. A. Komarov, “Best Approximation Rate of Constants by Simple Partial Fractions and Chebyshev Alternance”, Math. Notes, 97:5 (2015), 725–737  mathnet  crossref  crossref  mathscinet  isi  elib
    3. M. A. Komarov, “A criterion for the best uniform approximation by simple partial fractions in terms of alternance”, Izv. Math., 79:3 (2015), 431–448  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. M. A. Komarov, “A criterion for the best uniform approximation by simple partial fractions in terms of alternance. II”, Izv. Math., 81:3 (2017), 568–591  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    6. M. A. Komarov, “Estimates of the Best Approximation of Polynomials by Simple Partial Fractions”, Math. Notes, 104:6 (2018), 848–858  mathnet  crossref  crossref  isi  elib
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