V. I. Danchenko, E. N. Kondakova, “Chebyshev's alternance in the approximation of constants by simple partial fractions”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 86–96; Proc. Steklov Inst. Math., 270 (2010), 80

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 270, Pages 86–96 (Mi tm3012)

This article is cited in 20 scientific papers (total in 20 papers)

Chebyshev's alternance in the approximation of constants by simple partial fractions

V. I. Danchenko, E. N. Kondakova

Chair of Functional Analysis and Its Applications, Vladimir State University, Vladimir, Russia

Full-text PDF (224 kB) Citations (20)

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Abstract: Uniform approximation of real constants by simple partial fractions on a closed interval of the real axis is studied. It is proved that a simple partial fraction of best approximation of degree

n

$n$ for a constant is unique and coincides with this constant at

n

$n$ nodes lying on the interval; moreover, there is a Chebyshev alternance consisting of

n + 1

$n+1$ points.

Received in February 2010

English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 270, Pages 80–90
DOI: https://doi.org/10.1134/S0081543810030065

Bibliographic databases:

Document Type: Article

UDC: 517.538.52+517.538.7

Language: Russian

Citation: V. I. Danchenko, E. N. Kondakova, “Chebyshev's alternance in the approximation of constants by simple partial fractions”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 86–96; Proc. Steklov Inst. Math., 270 (2010), 80–90

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tm3012

https://www.mathnet.ru/eng/tm/v270/p86

This publication is cited in the following 20 articles:

A. P. Loktionov, “Chebyshev Alternance when Approximating Initial Conditions of the Inverse Cauchy Problem”, Proceedings of the SWSU, 25:3 (2022), 86
M. A. Komarov, “Extremal Properties of Logarithmic Derivatives of Polynomials”, J Math Sci, 250:1 (2020), 1
Komarov M.A., “Approximation to Constant Functions By Electrostatic Fields Due to Electrons and Positrons”, Lobachevskii J. Math., 40:1, SI (2019), 79–84
V. I. Danchenko, E. N. Kondakova, “Algorithm for Constructing Simple Partial Fractions of the Best Approximation of Constants”, J Math Sci, 239:3 (2019), 299
M. A. Komarov, “Approximation by linear fractional transformations of simple partial fractions and their differences”, Russian Math. (Iz. VUZ), 62:3 (2018), 23–33
M. A. Komarov, “On approximation by special differences of simplest fractions”, St. Petersburg Math. J., 30:4 (2019), 655–665
V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Extremal and approximative properties of simple partial fractions”, Russian Math. (Iz. VUZ), 62:12 (2018), 6–41
M. A. Komarov, “Criteria for the Best Approximation by Simple Partial Fractions on Semi-Axis and Axis”, J Math Sci, 235:2 (2018), 168
M. A. Komarov, “A criterion for the best uniform approximation by simple partial fractions in terms of alternance. II”, Izv. Math., 81:3 (2017), 568–591
M. A. Komarov, “Best Approximation Rate of Constants by Simple Partial Fractions and Chebyshev Alternance”, Math. Notes, 97:5 (2015), 725–737
M. A. Komarov, “A criterion for the best uniform approximation by simple partial fractions in terms of alternance”, Izv. Math., 79:3 (2015), 431–448
M. A. Komarov, “An Analog of the Haar Condition for Simple Partial Fractions”, J Math Sci, 208:2 (2015), 174
M. A. Komarov, “A criterion for the solvability of the multiple interpolation problem by simple partial fractions”, Siberian Math. J., 55:4 (2014), 611–621
Chunaev P., “Least Deviation of Logarithmic Derivatives of Algebraic Polynomials From Zero”, J. Approx. Theory, 185 (2014), 98–106
M. A. Komarov, “A Criterion for the Best Approximation of Constants by Simple Partial Fractions”, Math. Notes, 93:2 (2013), 250–256
M. A. Komarov, “An example of nonuniqueness of a simple partial fraction of the best uniform approximation”, Russian Math. (Iz. VUZ), 57:9 (2013), 22–30
V. I. Danchenko, E. N. Kondakova, “Criterion for the appearance of singular nodes under interpolation by simple partial fractions”, Proc. Steklov Inst. Math., 278 (2012), 41–50
M. A. Komarov, “Examples related to best approximation by simple partial fractions”, J Math Sci, 184:4 (2012), 509
M. A. Komarov, “Interpolation of rational functions by simple partial fractions”, J Math Sci, 181:5 (2012), 600
M. A. Komarov, “Uniqueness of a simple partial fraction of best approximation”, J Math Sci, 175:3 (2011), 284

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

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