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Stieltjes-type polynomials on the unit circle

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URI: http://hdl.handle.net/10016/6274
ISSN: 0025-5718 (Print)
ISSN: 1088-6842 (Online)
DOI: 10.1090/S0025-5718-08-02195-9
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stieltjes_lagomasino_moc_2009.pdf (268.01 KB)
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2009-04
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American Mathematical Society
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Abstract
Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carathéodory function. In turn, this is used to give an estimate of the rate of convergence of certain quadrature formulae that resemble the Gauss-Kronrod rule, provided that the integrand is analytic in a neighborhood of T.
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29 pages, no figures.-- MSC2000 codes: Primary 65D32, 42A10, 42C05; Secondary 30E20.
MR#: MR2476567
Keywords
Quadrature rules on the unit circle, Para-orthogonal polynomials, Stieltjes polynomials, Gauss-Kronrod quadrature
Bibliographic citation
Mathematics of Computation, 2009, vol. 78, p. 969-997
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