The approximation of Cauchy-type integrals by some kinds of interpolatory splines

DOI10.1016/0021-9045(82)90040-5zbMath0497.41006OpenAlexW1966171263MaRDI QIDQ1170707

Chien-Ke Lu

Publication date: 1982

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(82)90040-5

zbMATH Keywords

error estimatescubic splinesinterpolating splineCauchy-type integralsquadratic spline

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spline approximation (41A15) Integral equations with kernels of Cauchy type (45E05)

Related Items (9)

Numerical solution of certain Cauchy singular integral equations using a collocation scheme ⋮ An efficient method for approximate solution of a singular integral equation with Cauchy kernel ⋮ Reproducing kernel method of solving singular integral equation with cosecant kernel ⋮ Reproducing kernel method for solving Fredholm integro-differential equations with weakly singularity ⋮ Approximate solution of periodic Riemann boundary value problem for analytic functions ⋮ A new efficient method with error analysis for solving the second kind Fredholm integral equation with Cauchy kernel ⋮ Numerical integration based on approximating splines ⋮ Spline approximate solution for doubly periodic Riemann boundary value problem ⋮ The complex spline approximation of singular integral operators over an open arc.

Cites Work

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• A class of quadrature formulas of Chebyshev type for singular integrals
• Error analysis for interpolating complex cubic splines with deficiency 2
• On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals
• Quadratic splines
• Properties of analytic splines. I: Complex polynomial splines
• Complex polynomial splines on the unit circle
• An algorithm for the numerical evaluation of certain Cauchy principal value integrals
• Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals
• Complex Cubic Splines
• The Numerical Evaluation of the Cauchy Transform on Simple Closed Curves

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