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

DOI10.1007/BF02786642zbMath1020.41019OpenAlexW2014099887MaRDI QIDQ698309

Manuel Bello-Hernández, Guillermo López Lagomasino, Bernardo de la Calle Ysern, José J. Guadalupe Hernandez

Publication date: 13 May 2003

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02786642

zbMATH Keywords

orthogonal polynomialsMarkov functionsPadé-type approximantsGauss-Kronrod quadratureStieltjes polynomials

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Padé approximation (41A21) Approximate quadratures (41A55)

Related Items (3)

The use of rational functions in numerical quadrature ⋮ Stieltjes-type polynomials on the unit circle ⋮ On certain symmetric strong distributions, two-point Padé approximation and related quadratures

Cites Work

• On the asymptotic behaviour of functions of the second kind and Stieltjes polynomials and on the Gauss-Kronrod quadrature formulas
• Error bounds for Gauss-Kronrod quadrature formulae of analytic functions
• Padé-type approximants of Markov and meromorphic functions
• Extremal polynomials with preassigned zeros and rational approximants
• Multipoint Padé-type approximants. Exact rate of convergence
• Asymptotic properties of Stieltjes polynomials and Gauss-Kronrod quadrature formulae
• Asymptotic behaviour of Stieltjes polynomials for ultraspherical weight functions
• Stieltjes polynomials and functions of the second kind
• ON ASYMPTOTIC PROPERTIES OF POLYNOMIALS ORTHOGONAL ON THE CIRCLE WITH WEIGHTS NOT SATISFYING SZEGÖ'S CONDITION
• Stieltjes Polynomials and Related Quadrature Rules
• Some New Formulae for the Stieltjes Polynomials Relative to Classical Weight Functions
• Positivity of the Weights of Extended Gauss-Legendre Quadrature Rules
• Orthogonal polynomials
• Ultraspherical Gauss--Kronrod Quadrature Is Not Possible for $\lambda > 3$
• Stieltjes polynomials and Lagrange interpolation
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