An automatic quadrature for Cauchy principal value integrals

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) . After subtracting out the singularity, we approximate the function f(t) by a sum of Chebyshev polynomials whose coefficients are computed using the FTT. 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.