Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules

DOI10.1007/s00211-017-0901-yzbMath1384.41022OpenAlexW2679179110MaRDI QIDQ1692299

Miodrag M. Spalević, Bernardo de la Calle Ysern

Publication date: 26 January 2018

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-017-0901-y

zbMATH Keywords

numerical integrationStieltjes polynomialKronrod method

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Approximate quadratures (41A55)

Related Items (2)

On the computation of Patterson-type quadrature rules ⋮ Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind

Uses Software

• QUADPACK
• OPQ
• EXTEND

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New block quadrature rules for the approximation of matrix functions
• Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
• Gauss-Kronrod quadrature formulae. A survey of fifty years of research
• Internality of generalized averaged Gauss rules and their truncations for Bernstein-Szegő weights
• Generalized averaged Szegő quadrature rules
• Truncated generalized averaged Gauss quadrature rules
• Suboptimal Kronrod extension formulae for numerical quadrature
• On the asymptotic behaviour of functions of the second kind and Stieltjes polynomials and on the Gauss-Kronrod quadrature formulas
• Modified optimal quadrature extensions
• Stieltjes polynomials and Gauss-Kronrod quadrature for Jacobi weight functions
• A historical note on Gauss-Kronrod quadrature
• Stieltjes polynomials and functions of the second kind
• Quadrature formulas for Fourier coefficients
• Calculation of Radau-Kronrod and Lobatto-Kronrod quadrature formulas
• A note on generalized averaged Gaussian formulas
• On generalized averaged Gaussian formulas. II
• Stieltjes-type polynomials on the unit circle
• Addition of Points to Gauss–Laguerre Quadrature Formulas
• On generalized averaged Gaussian formulas
• Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle
• Stieltjes Polynomials and Related Quadrature Rules
• Calculation of Gauss-Kronrod quadrature rules
• An algorithm for generating interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions
• Algorithm 672: generation of interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions
• Anti-Gaussian quadrature formulas
• Ultraspherical Gauss--Kronrod Quadrature Is Not Possible for $\lambda > 3$
• Computation of Gauss-Kronrod quadrature rules
• Optimal extension of the Szeg  quadrature
• Ultraspherical Stieltjes Polynomials and Gauss–Kronrod Quadrature Behave Nicely for $\lambda< 0$
• The Optimum Addition of Points to Quadrature Formulae
• An overview of the computational aspects of Kronrod quadrature rules
• A connection between quadrature formulas on the unit circle and the interval \([-1,1\)]

This page was built for publication: Modified Stieltjes polynomials and Gauss-Kronrod quadrature rules