This article is cited in 11 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.

UDC: 517.538

Received: 19.06.2012

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

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