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Asymptotics for Stieltjes polynomials, Padé-type approximants, and Gauss-Kronrod quadrature

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URI: https://hdl.handle.net/10016/6328
ISSN: 0021-7670 (Print)
ISSN: 1565-8538 (Online)
DOI: 10.1007/BF02786642
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2002-12
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Springer
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Abstract
We study the asymptotic properties of Stieltjes polynomials outside the support of the measure as well as the asymptotic behaviour of their zeros. These properties are used to estimate the rate of convergence of sequences of rational functions, whose poles are partially fixed, which approximate Markovtype functions. An estimate for the speed of convergence of the Gauss-Kronrod quadrature formula in the case of analytic functions is also given.
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23 pages, 1 figure.-- MSC1991 codes: Primary: 41A21, 42C05; Secondary: 30E10.
MR#: MR1894475 (2002m:41021)
Zbl#: Zbl 1020.41019
Keywords
Orthogonal polynomials, Padé-type approximation, Stieltjes polynomials, Gauss-Kronrod quadrature
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Journal d'Analyse Mathématique, 2002, vol. 86, n. 1, p. 1-23
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