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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2018, Volume 104, Issue 6, Pages 851–862 (Mi mz11224)

Estimates of the Best Approximation of Polynomials by Simple Partial Fractions

M. A. Komarov

Abstract: 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.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00744 This work was supported by the Russian Foundation for Basic Research under grant 18-01-00744.

DOI: https://doi.org/10.4213/mzm11224

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English version:
Mathematical Notes, 2018, 104:6, 848–858

Bibliographic databases:

UDC: 517.538
Revised: 25.12.2017

Citation: M. A. Komarov, “Estimates of the Best Approximation of Polynomials by Simple Partial Fractions”, Mat. Zametki, 104:6 (2018), 851–862; Math. Notes, 104:6 (2018), 848–858

Citation in format AMSBIB
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