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This article is cited in 3 scientific papers (total in 3 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
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.
DOI:
https://doi.org/10.4213/sm3905
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English version:
Sbornik: Mathematics, 2008, 199:2, 207–228
Bibliographic databases:
    
UDC:
517.518.82
MSC: Primary 41A05, 41A10, 41A50; Secondary 65D05, 65D32
Received: 07.06.2007 and 06.11.2007
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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Linking options:
http://mi.mathnet.ru/eng/msb3905https://doi.org/10.4213/sm3905 http://mi.mathnet.ru/eng/msb/v199/i2/p49
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This publication is cited in the following articles:
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V. I. Lebedev, “O trigonometricheskoi forme chebyshevskikh teorem ob alternanse i fazovom iteratsionnom metode nakhozhdeniya nailuchshikh s vesom priblizhenii”, Ufimsk. matem. zhurn., 1:4 (2009), 110–118
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Lebedev V.I., Bogatyrev A.B., Nechepurenko Yu.M., “Optimal methods in problems of computational mathematics”, Russian J. Numer. Anal. Math. Modelling, 25:5 (2010), 453–475
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A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048
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