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Sbornik: Mathematics, 2004, Volume 195, Issue 10, Pages 1413–1459
DOI: https://doi.org/10.1070/SM2004v195n10ABEH000852
(Mi sm852)
 

This article is cited in 7 scientific papers (total in 8 papers)

Extremal polynomials and methods of optimization of numerical algorithms

V. I. Lebedev

Russian Research Centre "Kurchatov Institute"
References:
Abstract: Chebyshëv–Markov–Bernstein–Szegö polynomials $C_n(x)$ extremal on $[-1,1]$ with weight functions $w(x)=(1+x)^\alpha(1- x)^\beta/\sqrt{S_l(x)}$ where $\alpha,\beta=0,\frac12$ and $S_l(x)=\prod_{k=1}^m(1-c_kT_{l_k}(x))>0$ are considered. A universal formula for their representation in trigonometric form is presented. Optimal distributions of the nodes of the weighted interpolation and explicit quadrature formulae of Gauss, Markov, Lobatto, and Rado types are obtained for integrals with weight $p(x)=w^2(x)(1-x^2)^{-1/2}$. The parameters of optimal Chebyshëv iterative methods reducing the error optimally by comparison with the initial error defined in another norm are determined. For each stage of the Fedorenko–Bakhvalov method iteration parameters are determined which take account of the results of the previous calculations. Chebyshëv filters with weight are constructed. Iterative methods of the solution of equations containing compact operators are studied.
Received: 26.02.2004
Bibliographic databases:
UDC: 517.518.8+519.6
MSC: Primary 41A50, 65D32, 65F10; Secondary 26C05
Language: English
Original paper language: Russian
Citation: V. I. Lebedev, “Extremal polynomials and methods of optimization of numerical algorithms”, Sb. Math., 195:10 (2004), 1413–1459
Citation in format AMSBIB
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\by V.~I.~Lebedev
\paper Extremal polynomials and methods of optimization of numerical algorithms
\jour Sb. Math.
\yr 2004
\vol 195
\issue 10
\pages 1413--1459
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\crossref{https://doi.org/10.1070/SM2004v195n10ABEH000852}
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Linking options:
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  • https://doi.org/10.1070/SM2004v195n10ABEH000852
  • https://www.mathnet.ru/eng/sm/v195/i10/p21
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:1075
    Russian version PDF:463
    English version PDF:31
    References:78
    First page:1
     
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