Abstract:
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, interpolation.
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