Geodesic
Estimates of the Best Approximation of Polynomials by Simple Partial Fractions
Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 851-862.

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An asymptotics of the error of interpolation of real constants at Chebyshev nodes is obtained. Some well-known estimates of the best approximation by simple partial fractions (logarithmic derivatives of algebraic polynomials) of real constants in the closed interval $[-1,1]$ and complex constants in the unit disk are refined. As a consequence, new estimates of the best approximation of real polynomials on closed intervals of the real axis and of complex polynomials on arbitrary compact sets are obtained.
Keywords: simple partial fraction, approximation, estimate, best approximation. 
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M. A. Komarov. Estimates of the Best Approximation of Polynomials by Simple Partial Fractions. Matematičeskie zametki, Tome 104 (2018) no. 6, pp. 851-862. http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a4/

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