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Sbornik: Mathematics, 2008, Volume 199, Issue 2, Pages 207–228
DOI: https://doi.org/10.1070/SM2008v199n02ABEH003916 (Mi sm3905) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Finding polynomials of best approximation with weight

V. I. Lebedevab

a Russian Research Centre "Kurchatov Institute"
b Institute of Numerical Mathematics, Russian Academy of Sciences
English version PDF (475 kB) Citations (5)
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DOI: https://doi.org/10.1070/SM2008v199n02ABEH003916
Abstract: A new iterative method for finding the parameters of polynomials of best approximation with weight in $C[-1,1]$ is presented. It is based on the representation of the error in the trigonometric form in terms of the phase function. The iterative method of finding the corrections to the phase functions that determine the joint motion of the zeros and the $e$-points of the error is based on inverse analysis, perturbation theory, and asymptotic formulae for extremal polynomials.
Bibliography: 24 titles.
Received: 07.06.2007 and 06.11.2007
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 2, Pages 49–70
DOI: https://doi.org/10.4213/sm3905
Bibliographic databases:
UDC: 517.518.82
MSC: Primary 41A05, 41A10, 41A50; Secondary 65D05, 65D32
Language: English
Original paper language: Russian
Citation: V. I. Lebedev, “Finding polynomials of best approximation with weight”, Mat. Sb., 199:2 (2008), 49–70; Sb. Math., 199:2 (2008), 207–228
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v199/i2/p49
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:687
    Russian version PDF:295
    English version PDF:7
    References:73
    First page:7
     
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