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. 
@article{MZM_2018_104_6_a4,
     author = {M. A. Komarov},
     title = {Estimates of the {Best} {Approximation} of {Polynomials} by {Simple} {Partial} {Fractions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {851--862},
     publisher = {mathdoc},
     volume = {104},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_6_a4/}
}
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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/