Geodesic
A Criterion for the Best Approximation of Constants by Simple Partial Fractions
Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 209-215.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of the best uniform approximation of a real constant $c$ by real-valued simple partial fractions $R_n$ on a closed interval of the real axis is considered. For sufficiently small (in absolute value) $c$, $|c|\leq c_n$, it is proved that $R_n$ is a fraction of best approximation if, for the difference $R_n-c$, there exists a Chebyshev alternance of $n+1$ points on a closed interval. A criterion for best approximation in terms of alternance is stated.
Keywords: best uniform approximation of a real constant, best approximation by simple partial fractions, Chebyshev alternance
Mots-clés : interpolation. 
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M. A. Komarov. A Criterion for the Best Approximation of Constants by Simple Partial Fractions. Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 209-215. http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a5/

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