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Mathematics of Computation

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An automatic quadrature for Cauchy principal value integrals

Authors: Takemitsu Hasegawa and Tatsuo Torii
Journal: Math. Comp. 56 (1991), 741-754
MSC: Primary 65D32
MathSciNet review: 1068816
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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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Keywords: Cauchy principal value integral, automatic integration, Chebyshev interpolation
Article copyright: © Copyright 1991 American Mathematical Society

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