Calle Ysern, Bernardo de laLópez Lagomasino, GuillermoReichel, Lothar2010-01-052010-01-052009-04Mathematics of Computation, 2009, vol. 78, p. 969-9970025-5718 (Print)1088-6842 (Online)https://hdl.handle.net/10016/627429 pages, no figures.-- MSC2000 codes: Primary 65D32, 42A10, 42C05; Secondary 30E20.MR#: MR2476567Stieltjes-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.application/pdfeng© American Mathematical SocietyQuadrature rules on the unit circlePara-orthogonal polynomialsStieltjes polynomialsGauss-Kronrod quadratureresearch articleMatemáticas10.1090/S0025-5718-08-02195-9open access