An automatic quadrature for Cauchy principal value integrals

Hasegawa, Takemitsu; Torii, Tatsuo

doi:10.1090/S0025-5718-1991-1068816-1

An automatic quadrature for Cauchy principal value integrals
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by Takemitsu Hasegawa and Tatsuo Torii PDF

Math. Comp. 56 (1991), 741-754 Request permission

Abstract:

An automatic quadrature is presented for computing Cauchy principal value integrals $Q(f;c) = \fint _a^bf(t)/(t-c) dt, a < c < b$, for smooth functions $f(t)$. After subtracting out the singularity, we approximate the function $f(t)$ by a sum of Chebyshev polynomials whose coefficients are computed using the FFT. The evaluations of $Q(f;c)$ for a set of values of c in (a, b) are efficiently accomplished with the same number of function evaluations. Numerical examples are also given.

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