Roundoff errors in the problem of computing Cauchy principal value integrals

Details Roundoff errors in the problem of computing Cauchy principal value integrals Roundoff errors in the problem of computing Cauchy principal value integrals

2011-11-09

arxiv.org/abs/1111.2283v1

Mathematics

Numerical Analysis

Scientific paper

We show that, when handled properly, the Cauchy principal value integral
$\cpint_{a}^{b}f(x)(x-\tau)^{-1} dx\,\,\,(a < \tau < b)$ can be computed very
easily and accurately using any reliable adaptive quadrature. We give detailed
estimations of the roundoff errors in the case the function $f$ has bounded
first derivative in the interval $[a,b]$.

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