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Tr. Mat. Inst. Steklova, 2010, Volume 270, Pages 86–96 (Mi tm3012)  

This article is cited in 12 scientific papers (total in 12 papers)

Chebyshev's alternance in the approximation of constants by simple partial fractions

V. I. Danchenko, E. N. Kondakova

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

Abstract: Uniform approximation of real constants by simple partial fractions on a closed interval of the real axis is studied. It is proved that a simple partial fraction of best approximation of degree $n$ for a constant is unique and coincides with this constant at $n$ nodes lying on the interval; moreover, there is a Chebyshev alternance consisting of $n+1$ points.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 270, 80–90

Bibliographic databases:

UDC: 517.538.52+517.538.7
Received in February 2010

Citation: V. I. Danchenko, E. N. Kondakova, “Chebyshev's alternance in the approximation of constants by simple partial fractions”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 86–96; Proc. Steklov Inst. Math., 270 (2010), 80–90

Citation in format AMSBIB
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\paper Chebyshev's alternance in the approximation of constants by simple partial fractions
\inbook Differential equations and dynamical systems
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\pages 86--96
\publ MAIK Nauka/Interperiodica
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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. V. I. Danchenko, E. N. Kondakova, “Criterion for the appearance of singular nodes under interpolation by simple partial fractions”, Proc. Steklov Inst. Math., 278 (2012), 41–50  mathnet  crossref  mathscinet  isi  elib  elib
    2. M. A. Komarov, “A Criterion for the Best Approximation of Constants by Simple Partial Fractions”, Math. Notes, 93:2 (2013), 250–256  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. M. A. Komarov, “An example of nonuniqueness of a simple partial fraction of the best uniform approximation”, Russian Math. (Iz. VUZ), 57:9 (2013), 22–30  mathnet  crossref
    4. M. A. Komarov, “A criterion for the solvability of the multiple interpolation problem by simple partial fractions”, Siberian Math. J., 55:4 (2014), 611–621  mathnet  crossref  mathscinet  isi
    5. 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
    6. 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
    7. 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
    8. 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
    9. M. A. Komarov, “Approximation by linear fractional transformations of simple partial fractions and their differences”, Russian Math. (Iz. VUZ), 62:3 (2018), 23–33  mathnet  crossref  isi
    10. M. A. Komarov, “O priblizhenii spetsialnymi raznostyami naiprosteishikh drobei”, Algebra i analiz, 30:4 (2018), 47–60  mathnet
    11. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    12. Komarov M.A., “Approximation to Constant Functions By Electrostatic Fields Due to Electrons and Positrons”, Lobachevskii J. Math., 40:1, SI (2019), 79–84  crossref  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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