Asymptotic expansions and fast computation of oscillatory Hilbert transforms
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Publication:1944001
DOI10.1007/s00211-012-0501-9zbMath1263.65131arXiv1112.2282OpenAlexW1974018534WikidataQ117717442 ScholiaQ117717442MaRDI QIDQ1944001
Lun Zhang, Daan Huybrechs, Haiyong Wang
Publication date: 3 April 2013
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1112.2282
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Cites Work
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- Error bounds for approximation in Chebyshev points
- A method for numerical integration on an automatic computer
- The Euler-Maclaurin expansion for the Cauchy principal value integral
- Efficient Filon-type methods for \(\int_a^b f(x)\,e^{i\omega g(x)}\, dx\)
- On the evaluation of Cauchy principal value integrals of oscillatory functions
- Complex Gaussian quadrature of oscillatory integrals
- Uniform approximations to Cauchy principal value integrals of oscillatory functions
- Numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures
- Quadrature formulas for oscillatory integral transforms
- On the computation of Fourier transforms of singular functions
- The Euler-Maclaurin expansion and finite-part integrals
- On quadrature for Cauchy principal value integrals of oscillatory functions.
- A method to generate generalized quadrature rules for oscillatory integrals
- Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach
- Fast integration of rapidly oscillatory functions
- Relative error propagation in the recursive solution of linear recurrence relations
- On quadrature methods for highly oscillatory integrals and their implementation
- Asymptotic Approximations of Integrals
- Complex Gaussian quadrature for oscillatory integral transforms
- Computing the Hilbert transform and its inverse
- GMRES for the Differentiation Operator
- Stability and error estimates for Filon-Clenshaw-Curtis rules for highly oscillatory integrals
- On the Evaluation of Highly Oscillatory Integrals by Analytic Continuation
- Quadrature Formulae for Cauchy Principal Value Integrals of Oscillatory Kind
- Asymptotic Expansion of the Hilbert Transform
- On the null-field equations for water-wave radiation problems
- Procedures for Computing One- and Two-Dimensional Integrals of Functions with Rapid Irregular Oscillations
- Barycentric Lagrange Interpolation
- Integrals with a large parameter: Hilbert transforms
- An Automatic Quadrature for Cauchy Principal Value Integrals
- Efficient quadrature of highly oscillatory integrals using derivatives
- Numerical Methods for Special Functions
- Moment-free numerical integration of highly oscillatory functions
- Numerical solution of second-order linear difference equations
- Implementing Clenshaw-Curtis quadrature, I methodology and experience
