On the convergence of the Gauss quadrature rules for Cauchy principal value integrals

zbMath0638.65016MaRDI QIDQ1099579

Giuseppe Mastroianni, Giuliana Criscuolo

Publication date: 1986

Published in: Ricerche di Matematica (Search for Journal in Brave)

zbMATH Keywords

convergenceCauchy principal value integralsGaussian quadrature rulesgeneralized smooth Jacobi weight

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 (17)

Filtered integration rules for finite weighted Hilbert transforms ⋮ Two new formulas for the numerical evaluation of the Hilbert transform ⋮ Convergence of Gauss-Lobatto type quadrature formulas for the evaluation of principal value singular integrals ⋮ On the convergence of a rule by Monegato for the numerical evaluation of Cauchy principal value integrals ⋮ Convergence of Gauss type product formulas for the evaluation of two- dimensional Cauchy principal value integrals ⋮ Convergence of Gaussian formulas for the calculation of the derivatives of Cauchy principal value integrals ⋮ A bound for generalized Jacobi functions of the second kind ⋮ An algorithm for the numerical resolution of a class of singular integral equations ⋮ New error bounds for modified quadrature formulas for Cauchy principal value integrals ⋮ Some numerical algorithms to evaluate Hadamard finite-part integrals ⋮ On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals ⋮ On quadrature for Cauchy principal value integrals of oscillatory functions. ⋮ On the convergence of Turán type rules for Cauchy principal value integrals ⋮ Convergence of Extended Lagrange Interpolation ⋮ On the evaluation of one-dimensional Cauchy principal value integrals by rules based on cubic spline interpolation ⋮ The numerical evaluation of Cauchy principal value integrals with non-standard weight functions ⋮ Approximation of the Hilbert transform on the real semiaxis using Laguerre zeros

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