Journal ArticleDOI
A Note on Quadrature Formulae for Cauchy Principal Value Integrals
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This article is published in Ima Journal of Applied Mathematics.The article was published on 1980-12-01. It has received 11 citations till now. The article focuses on the topics: Gauss–Jacobi quadrature & Clenshaw–Curtis quadrature.read more
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The numerical evaluation of one-dimensional Cauchy principal value integrals
TL;DR: This paper examines the numerical integration (in the Cauchy principal value sense) of functions having (several) first order real poles and proposes an alternative algorithm for the numerical evaluation of integrals of the form.
Journal ArticleDOI
An automatic quadrature for Cauchy principal value integrals
Takemitsu Hasegawa,Tatsuo Torii +1 more
TL;DR: In this paper, an automatic quadrature is presented for computing Cauchy principal value integrals Q(f; c) = Faf(t)/(t c) dt, a < c < b, for smooth functions f(t).
Journal ArticleDOI
Uniform approximations to finite Hilbert transform and its derivative
TL;DR: In this article, interpolating a smooth function f(t) at abscissae in the interval of integration is shown to be essential for uniformly approximating Cauchy principal value integrals and Hadamard finite part integrals.
Journal ArticleDOI
Quadrature formulae for Cauchy principal value integrals of oscillatory kind
TL;DR: In this paper, the evaluation numerique d'une integrale #7B-F −1 1 exp(iωx)f(x)dx ou f possede un pole simple dans l'intervalle [−1, 1].
Journal ArticleDOI
Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach
TL;DR: In this paper, the numerical evaluation of Hilbert transforms on the real line for functions that exhibit oscillatory behavior is investigated and a fairly robust numerical procedure is developed that is based on the use of convergence accelerator techniques.