Approximation of the Hilbert Transform on the real line using Hermite zeros

DOI10.1090/S0025-5718-01-01338-2zbMath0993.65145OpenAlexW2018007544MaRDI QIDQ4529711

Biancamaria Della Vecchia, Giuseppe Mastroianni, Maria Carmela De Bonis

Publication date: 6 May 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01338-2

zbMATH Keywords

algorithmconvergencecomparison of methodsnumerical examplesHilbert transformorthonormal polynomialsGaussian quadrature rulesproduct quadrature rules

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10)

Related Items (9)

Quadrature rules for \(L^1\)-weighted norms of orthogonal polynomials ⋮ A method to evaluate the Hilbert transform on (\(0, +\infty \)) ⋮ On the numerical solution of Fredholm integral equations on unbounded intervals ⋮ Numerical methods for some special Fredholm integral equations on the real line. ⋮ Extended Lagrange interpolation on the real line ⋮ A Nyström method for Fredholm integral equations on the real line ⋮ Multi-domain spectral approach for the Hilbert transform on the real line ⋮ Approximation methods and stability of singular integral equations for Freud exponential weights on the line ⋮ Approximation of the Hilbert transform on the real semiaxis using Laguerre zeros

Uses Software

• Algorithm 680

Cites Work

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• On the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals
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• On the Convergence of Product Formulas for the Evaluation of Certain Two-Dimensional Cauchy Principal Value Integrals
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• Convergence of Product Integration Rules Over (0, ∞) for Functions with Weak Singularities at the Origin
• Nystroem interpolants based on zeros of Laguerre polynomials for some Weiner-Hopf equations
• Algorithm 680: evaluation of the complex error function
• Anwendung der Rechteckregel auf die reelle Hilberttransformation mit unendlichem Intervall
• Mean Cesaro Summability of Laguerre and Hermite Series

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