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This article is cited in 7 scientific papers (total in 7 papers)
A Criterion for the Best Approximation of Constants by Simple Partial Fractions
M. A. Komarov Vladimir State University
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.
Received: 04.07.2011 Revised: 09.11.2011
Citation:
M. A. Komarov, “A Criterion for the Best Approximation of Constants by Simple Partial Fractions”, Mat. Zametki, 93:2 (2013), 209–215; Math. Notes, 93:2 (2013), 250–256
Linking options:
https://www.mathnet.ru/eng/mzm9203https://doi.org/10.4213/mzm9203 https://www.mathnet.ru/eng/mzm/v93/i2/p209
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Abstract page: | 592 | Full-text PDF : | 176 | References: | 84 | First page: | 49 |
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