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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 6, Pages 1404–1423 (Mi smj2615)  
This article is cited in 9 scientific papers (total in 9 papers)

Influence of the choice of Lagrange interpolation nodes on the exact and approximate values of the Lebesgue constants

I. A. Shakirov

Nabereznye Chelny Institute of Social-Pedagogical Technologies and Resources, Nabereznye Chelny, Russia
Full-text PDF (371 kB) Citations (9)
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Abstract: The behavior of the Lebesgue constants corresponding to two classical Lagrange interpolation polynomials is studied in dependence on the number of interpolation nodes uniformly distributed on the period divided into three classes. We obtain new exact and approximate formulas for the constants corresponding to each of these classes: the errors are estimated uniformly in the degree of a polynomial. Two standing problems are solved in interpolation theory that are connected with asymptotic equalities for Lebesgue constants.
Keywords: Lagrange polynomials, interpolation nodes, uniform convergence, Lebesgue constants, error of formulas.
Received: 27.05.2014
English version:
Siberian Mathematical Journal, 2014, Volume 55, Issue 6, Pages 1144–1160
DOI: https://doi.org/10.1134/S0037446614060184
Bibliographic databases:
Document Type: Article
UDC: 591.65
Language: Russian
Citation: I. A. Shakirov, “Influence of the choice of Lagrange interpolation nodes on the exact and approximate values of the Lebesgue constants”, Sibirsk. Mat. Zh., 55:6 (2014), 1404–1423; Siberian Math. J., 55:6 (2014), 1144–1160
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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