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

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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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     author = {M. A. Komarov},
     title = {A {Criterion} for the {Best} {Approximation} of {Constants} by {Simple} {Partial} {Fractions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {209--215},
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     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a5/}
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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/