Numerical integration based on quasi-interpolating splines

DOI10.1007/BF02238611zbMath0768.41026MaRDI QIDQ2366296

Elisabetta Santi, Vittoria Demichelis, Cattarina Dagnino

Publication date: 29 June 1993

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

numerical examplesCauchy principal value integralsproduct quadrature rulesquasi-interpolating splines

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Spline approximation (41A15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (26)

Application of approximating splines for the solution of Cauchy singular integral equations ⋮ Approximating the finite Hilbert transform via a companion of Ostrowski's inequality for function of bounded variation and applications ⋮ Bivariate quasi-interpolating splines with applications in numerical integration ⋮ Computational Aspects Of Numerical Integration Based On Optimal Nodal Splines ⋮ On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules ⋮ On the uniform convergence of Cauchy principal values of quasi-interpolating splines ⋮ The use of modified quasi-interpolatory splines for the solution of the Prandtl equation ⋮ On the numerical solution of the generalized Prandtl equation using variation-di/-minishing splines ⋮ On the evaluation of Cauchy principal value integrals by rules based on quasi-interpolating splines ⋮ Error bounds for spline-based quadrature methods for strongly singular integrals ⋮ Projector-splines in the numerical solution of integro-differential equations ⋮ Uniform convergence for cauchy principal value integrals of modified quasi-interpolatory splines^∗ ⋮ Error estimate and extrapolation of a quadrature formula derived from a quartic spline quasi-interpolant ⋮ Numerical evaluation of certain hypersingular integrals using refinable operators ⋮ Numerical integration based on bivariate quadratic spline quasi-interpolants on Powell-Sabin partitions ⋮ Numerical integration based on trivariate \(C ^{2}\) quartic spline quasi-interpolants ⋮ About some numerical approaches for mixed integral equations ⋮ Quasi-interpolatory splines based on Schoenberg points ⋮ Superconvergent spline quasi-interpolants and an application to numerical integration ⋮ Approximating the finite Hilbert transform via some companions of Ostrowski's inequalities ⋮ Efficient quadrature rules based on spline quasi-interpolation for application to IGA-BEMs ⋮ Product integration of singular integrands using quasi-interpolatory splines ⋮ Numerical evaluation of Cauchy principal value integrals based on local spline approximation operators ⋮ On spline quasi-interpolation through dimensions ⋮ An algorithm for numerical integration based on quasi-interpolating splines ⋮ Spline approximation with interpolation constraints for numerical integration

Cites Work

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• Product integration of singular integrands using quasi-interpolatory splines
• Numerical integration based on approximating splines
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• Product integration of piecewise continuous integrands based on cubic spline interpolation at equally spaced nodes
• On the convergence of spline product quadratures for Cauchy principal value integrals
• Local spline approximation methods
• A practical guide to splines
• Product integration of singular integrands based on cubic spline interpolation at equally spaced nodes
• On the evaluation of one-dimensional Cauchy principal value integrals by rules based on cubic spline interpolation
• An algorithm for numerical integration based on quasi-interpolating splines
• Piecewise-Polynomial Quadratures for Cauchy Singular Integrals

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