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Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 9, Pages 28–37 (Mi ivm8825)  

This article is cited in 8 scientific papers (total in 8 papers)

An example of nonuniqueness of a simple partial fraction of the best uniform approximation

M. A. Komarov

Chair of Functional Analysis and Applications, Vladimir State University, 87 Gor'kii str., Vladimir, 600000 Russia

Abstract: For arbitrary natural $n\ge2$ we construct an example of a real continuous function, for which there exist more than one simple partial fraction of order $\le n$ of the best uniform approximation on a segment of the real axis. We prove that even the Chebyshev alternance consisting of $n+1$ points does not guarantee the uniqueness of the best approximation fraction. The obtained results are generalizations of known nonuniqueness examples constructed for $n=2,3$ in the case of simple partial fractions of an arbitrary order $n$.

Keywords: simple partial fraction, approximation, uniqueness, alternance.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:9, 22–30

UDC: 517.538
Received: 19.06.2012

Citation: M. A. Komarov, “An example of nonuniqueness of a simple partial fraction of the best uniform approximation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 9, 28–37; Russian Math. (Iz. VUZ), 57:9 (2013), 22–30

Citation in format AMSBIB
\Bibitem{Kom13}
\by M.~A.~Komarov
\paper An example of nonuniqueness of a~simple partial fraction of the best uniform approximation
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 9
\pages 28--37
\mathnet{http://mi.mathnet.ru/ivm8825}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 9
\pages 22--30
\crossref{https://doi.org/10.3103/S1066369X13090041}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84894210191}


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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. 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
    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
    3. 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
    4. 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
    5. 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
    6. 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
    7. M. A. Komarov, “O priblizhenii spetsialnymi raznostyami naiprosteishikh drobei”, Algebra i analiz, 30:4 (2018), 47–60  mathnet
    8. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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