V. I. Danchenko, D. Ya. Danchenko, “Approximation by Simplest Fractions”, Mat. Zametki, 70:4 (2001), 553–559; Math. Notes, 70:4 (2001), 502

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Matematicheskie Zametki, 2001, Volume 70, Issue 4, Pages 553–559
DOI: https://doi.org/10.4213/mzm767 (Mi mzm767)

This article is cited in 41 scientific papers (total in 41 papers)

Approximation by Simplest Fractions

V. I. Danchenko, D. Ya. Danchenko

Vladimir State University

Full-text PDF (179 kB) Citations (41)

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DOI: https://doi.org/10.4213/mzm767

Abstract: In this paper, a number of problems concerning the uniform approximation of complex-valued continuous functions

f (z)

$f(z)$ on compact subsets of the complex plane by simplest fractions of the form

Θ_{n} (z) = \sum_{j = 1}^{n} 1 / (z - z_{j})

$\Theta _n(z)=\sum _{j=1}^n1/(z-z_j)$ are considered. In particular, it is shown that the best approximation of a function

f

$f$ by the fractions

Θ_{n}

$\Theta _n$ is of the same order of vanishing as the best approximations by polynomials of degree

$\le n$ .

Received: 19.10.2000

English version:
Mathematical Notes, 2001, Volume 70, Issue 4, Pages 502–507
DOI: https://doi.org/10.1023/A:1012328819487

Bibliographic databases:

UDC: 517.53

Language: Russian

Citation: V. I. Danchenko, D. Ya. Danchenko, “Approximation by Simplest Fractions”, Mat. Zametki, 70:4 (2001), 553–559; Math. Notes, 70:4 (2001), 502–507

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm767

https://doi.org/10.4213/mzm767

https://www.mathnet.ru/eng/mzm/v70/i4/p553

This publication is cited in the following 41 articles:

M. A. Komarov, “O skorosti interpolyatsii naiprosteishimi drobyami analiticheskikh funktsii s regulyarno ubyvayuschimi koeffitsientami”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 23:2 (2023), 157–168
P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
K. Shklyaev, “Approximation by sums of shifts and dilations of a single function and neural networks”, Journal of Approximation Theory, 291 (2023), 105915
P. A. Borodin, “Approximation by Simple Partial Fractions: Universal Sets of Poles”, Math. Notes, 111:1 (2022), 3–6
P. A. Borodin, K. S. Shklyaev, “Approximation by simple partial fractions in unbounded domains”, Sb. Math., 212:4 (2021), 449–474
P. A. Borodin, “Greedy approximation by arbitrary set”, Izv. Math., 84:2 (2020), 246–261
M. A. Komarov, “On the rate of approximation in the unit disc of $H^1$-functions by logarithmic derivatives of polynomials with zeros on the boundary”, Izv. Math., 84:3 (2020), 437–448
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
P. A. Borodin, “Approximation by Sums of the Form $\sum_k\lambda_kh(\lambda_kz)$ in the Disk”, Math. Notes, 104:1 (2018), 3–9
M. A. Komarov, “On approximation of the rational functions, whose integral is single-valued on $\mathbb{C}$, by differences of simplest fractions”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 63–71
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, “Estimates of the Best Approximation of Polynomials by Simple Partial Fractions”, Math. Notes, 104:6 (2018), 848–858
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
P. A. Borodin, “Approximation by sums of shifts of a single function on the circle”, Izv. Math., 81:6 (2017), 1080–1094
Yu. M. Nigmatyanova, “Numerical Analysis of the Method of Differentiation by Means of Real h-Sums”, J Math Sci, 224:5 (2017), 735
P. A. Borodin, “Approximation by simple partial fractions with constraints on the poles. II”, Sb. Math., 207:3 (2016), 331–341

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

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