On the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals

DOI10.2307/2007839zbMath0638.65017OpenAlexW4233394670MaRDI QIDQ3779649

Giuseppe Mastroianni, Giuliana Criscuolo

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2007839

zbMATH Keywords

convergenceasymptotic estimatesCauchy principal value integralsJacobi weightCauchy singular integralsinterpolatory product rules

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (24)

Filtered integration rules for finite weighted Hilbert transforms ⋮ An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on ℝ ⋮ Approximation of the Hilbert Transform on the real line using Hermite zeros ⋮ Uniform convergence of optimal order quadrature rules for Cauchy principal value integrals ⋮ On the convergence of a rule by Monegato for the numerical evaluation of Cauchy principal value integrals ⋮ The work of Philip Rabinowitz on numerical integration ⋮ The use of spline-on-spline for the approximation of Cauchy principal value integrals ⋮ Noninterpolatory Integration Rules for Cauchy Principal Value Integrals ⋮ Gaussian quadrature formulae of the third kind for Cauchy principal value integrals: Basic properties and error estimates ⋮ On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals ⋮ Gauss quadrature rules for Cauchy principal value integrals with wavelets ⋮ Spline approximations for Cauchy principal value integrals ⋮ On the convergence of spline product quadratures for Cauchy principal value integrals ⋮ Convergence and stability of a new quadrature rule for evaluating Hilbert transform ⋮ Convergence Results for Piecewise Linear Quadratures for Cauchy Principal Value Integrals ⋮ Numerical Evaluation of Cauchy Principal Value Integrals with Singular Integrands ⋮ On an interpolatory product rule for evaluating Cauchy principal value integrals ⋮ The numerical evaluation of Cauchy principal value integrals with non-standard weight functions ⋮ Spline product quadrature rules for Cauchy singular integrals ⋮ On the Convergence of Product Formulas for the Evaluation of Certain Two-Dimensional Cauchy Principal Value Integrals ⋮ Associated generalized Jacobi functions and polynomials ⋮ Approximation of the Hilbert transform on the real semiaxis using Laguerre zeros ⋮ Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach ⋮ Error estimates in the numerical evaluation of some BEM singular integrals

This page was built for publication: On the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals