Uniform convergence of optimal order quadrature rules for Cauchy principal value integrals

DOI10.1016/0377-0427(94)90086-8zbMath0821.41027OpenAlexW2091337501WikidataQ59411921 ScholiaQ59411921MaRDI QIDQ1893553

Kai Diethelm

Publication date: 3 October 1995

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

Full work available at URL: https://doi.org/10.1016/0377-0427(94)90086-8

zbMATH Keywords

uniform convergencespline interpolationquadrature formulaoptimal order of convergenceCauchy principal value integralsPeano constants

Mathematics Subject Classification ID

Approximate quadratures (41A55)

Related Items (10)

Filtered integration rules for finite weighted Hilbert transforms ⋮ New error bounds for modified quadrature formulas for Cauchy principal value integrals ⋮ Gaussian quadrature formulae of the third kind for Cauchy principal value integrals: Basic properties and error estimates ⋮ A definiteness criterion for linear functionals and its application to Cauchy principal value quadrature ⋮ Error bounds for spline-based quadrature methods for strongly singular integrals ⋮ On computing with the Hilbert spline transform ⋮ Numerical integration based on trivariate \(C ^{2}\) quartic spline quasi-interpolants ⋮ The Hilbert transform of cubic splines ⋮ BOUNDEDNESS AND UNIFORM NUMERICAL APPROXIMATION OF THE WEIGHTED HILBERT TRANSFORM ON THE REAL LINE ⋮ Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach

Uses Software

• Mathematica

Cites Work

• Spline product quadrature rules for Cauchy singular integrals
• Spline approximations for Cauchy principal value integrals
• Gauss Type Quadrature Rules for Cauchy Principal Value Integrals
• On the Numerical Evaluation of Singular Integrals of Cauchy Type
• On the Convergence of Some Cubic Spline Interpolation Schemes
• Piecewise-Polynomial Quadratures for Cauchy Singular Integrals
• On the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals
• Approximation by spline interpolating bases
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