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Mat. Sb., 2008, Volume 199, Number 2, Pages 49–70 (Mi msb3905)  

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

Full text: PDF file (727 kB)
References: PDF file   HTML file

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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  • https://doi.org/10.4213/sm3905
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  zmath
    2. 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  crossref  mathscinet  zmath  isi  elib  scopus
    3. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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