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

23 pages, 1 figure.-- MSC1991 codes: Primary: 41A21, 42C05; Secondary: 30E10.MR#: MR1894475 (2002m:41021)Zbl#: Zbl 1020.41019We 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.The work of M. Bello and J. J. Guadalupe was partially supported by DGES under grant PB96-0120-C03-02 and UR, AP-98/B12. The work of G. López was partially supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT.Publicad