Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes

DOI10.1007/s10543-015-0551-3zbMath1342.65102OpenAlexW2003779866MaRDI QIDQ285297

Miodrag M. Spalević, Aleksandar S. Cvetković

Publication date: 19 May 2016

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-015-0551-3

zbMATH Keywords

Gauss quadraturea posteriori error estimateVolterra integral equationsextension with multiple nodesGauss-Kronrod quadraturesKronrod extension

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Remainders in approximation formulas (41A80)

Uses Software

• Mathematica
• OrthogonalPolynomials
• OPQ
• HPGT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Calculation of Gauss quadratures with multiple free and fixed knots
• High-precision Gauss-Turán quadrature rules for Laguerre and Hermite weight functions
• Asymptotic representation of \(L_{p}\)-minimal polynomials, \(1 < p < \infty\)
• Construction of \(\sigma\)-orthogonal polynomials and Gaussian quadrature formulas
• Grauss-Kronrod quadrature formulae for weight functions of Bernstein- Szegö type
• On the remainder term for analytic functions of Gauss-Lobatto and Gauss- Radau quadratures
• Nonexistence of extended Gauss-Laguerre and Gauss-Hermite quadrature rules with positive weights
• \(S\)-orthogonality and construction of Gauss-Turán-type quadrature formulae
• Convergence of Gaussian quadrature formulas on infinite intervals
• Stieltjes polynomials and Gauss-Kronrod quadrature for Jacobi weight functions
• Symmetric Gauss-Lobatto and modified anti-Gauss rules
• Convergence of Gaussian quadrature formulas
• On stratified extensions of Gauss-Laguerre and Gauss-Hermite quadrature formulas
• A historical note on Gauss-Kronrod quadrature
• Calculation of Gaussian-type quadratures with multiple nodes
• Error bounds of the Micchelli-Sharma quadrature formula for analytic functions
• Quadrature formulas for Fourier coefficients
• A note on generalized averaged Gaussian formulas
• Estimating the error of Gauss-Turán quadrature formulas using their extensions
• Quadrature formulae
• Christoffel type functions for \(m\)-orthogonal polynomials
• On generalized averaged Gaussian formulas
• Gauss–Turán Quadrature Formulas: Asymptotics of Weights
• Stieltjes Polynomials and Related Quadrature Rules
• Calculation of Gauss-Kronrod quadrature rules
• On weight functions which admit explicit Gauss-Turán quadrature formulas
• Anti-Gaussian quadrature formulas
• Ultraspherical Gauss--Kronrod Quadrature Is Not Possible for $\lambda > 3$
• Computation of Gauss-Kronrod quadrature rules
• Kronrod extensions with multiple nodes of quadrature formulas for Fourier coefficients
• Error Bounds and Estimates for Gauss--Turán Quadrature Formulae of Analytic Functions
• Calculation of Gauss Quadrature Rules
• An overview of the computational aspects of Kronrod quadrature rules

This page was built for publication: Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes