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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 56 (1991), 741-754
- MSC: Primary 65D32
- DOI: https://doi.org/10.1090/S0025-5718-1991-1068816-1
- MathSciNet review: 1068816