Geodesic
An example of nonuniqueness of a simple partial fraction of the best uniform approximation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2013), pp. 28-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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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
Mots-clés : alternance. 
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     title = {An example of nonuniqueness of a~simple partial fraction of the best uniform approximation},
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M. A. Komarov. An example of nonuniqueness of a simple partial fraction of the best uniform approximation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2013), pp. 28-37. http://geodesic.mathdoc.fr/item/IVM_2013_9_a3/

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