On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities

DOI10.1016/J.CAM.2017.10.034zbMath1380.65058OpenAlexW2767434258MaRDI QIDQ679577

Haiyong Wang

Publication date: 11 January 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.10.034

zbMATH Keywords

convergence ratenumerical expampleClenshaw-Curtis quadratureChebyshev coefficientsendpoint singularities

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (12)

Numerical evaluation of oscillatory-singular integrals ⋮ Exponential convergence of the \textit{hp}-version of the composite Gauss-Legendre quadrature for integrals with endpoint singularities ⋮ Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation ⋮ Fast non-polynomial interpolation and integration for functions with logarithmic singularities ⋮ On the optimal convergence rates of Chebyshev interpolations for functions of limited regularity ⋮ Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities ⋮ Analysis of Error Localization of Chebyshev Spectral Approximations ⋮ Asymptotic coefficients and errors for Chebyshev polynomial approximations with weak endpoint singularities: effects of different bases ⋮ Comparisons of best approximations with Chebyshev expansions for functions with logarithmic endpoint singularities ⋮ Optimal error estimates for Chebyshev approximations of functions with endpoint singularities in fractional spaces ⋮ Upper bounds on list star chromatic index of sparse graphs ⋮ Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces

Uses Software

• DLMF
• Clenshaw-Curtis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Acceleration of Gauss-Legendre quadrature for an integrand with an endpoint singularity
• A method for numerical integration on an automatic computer
• Convergence acceleration of some Gaussian quadrature formulas for analytic functions
• The kink phenomenon in Fejér and Clenshaw-Curtis quadrature
• Fast construction of the Fejér and Clenshaw-Curtis quadrature rules
• Quadrature formulas obtained by variable transformation
• Asymptotic expansions of Gauss-Legendre quadrature rules for integrals with endpoint singularities
• Variable transformations and Gauss–Legendre quadrature for integrals with endpoint singularities
• Asymptotic Representations of Fourier Integrals and the Method of Stationary Phase
• Rates of Convergence of Gaussian Quadrature for Singular Integrands
• Rates of Convergence of Gauss, Lobatto, and Radau Integration Rules for Singular Integrands
• Generalized Gaussian Quadrature Rules for Systems of Arbitrary Functions
• On the Convergence Rates of Gauss and Clenshaw--Curtis Quadrature for Functions of Limited Regularity
• Clenshaw–Curtis and Gauss–Legendre Quadrature for Certain Boundary Element Integrals
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Asymptotic Error Estimates for the Gauss Quadrature Formula
• Error Estimation in the Clenshaw-Curtis Quadrature Formula
• Adjusted Forms of the Fourier Coefficient Asymptotic Expansion and Applications in Numerical Quadrature
• Gaussian integration of functions with branch point singularities
• Implementing Clenshaw-Curtis quadrature, I methodology and experience
• Coefficients in Series Expansions for Certain Classes of Functions
• The Evaluation and Estimation of the Coefficients in the Chebyshev Series Expansion of a Function
• Asymptotic expansions of Legendre series coefficients for functions with endpoint singularities

This page was built for publication: On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities