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

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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. 
@article{IVM_2013_9_a3,
     author = {M. A. Komarov},
     title = {An example of nonuniqueness of a~simple partial fraction of the best uniform approximation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {28--37},
     publisher = {mathdoc},
     number = {9},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_9_a3/}
}
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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/