Roundoff errors in the problem of computing Cauchy principal value integrals
For researchers needing to compute Cauchy principal value integrals, this work offers an easy-to-implement method with controlled accuracy, though it is incremental.
The paper investigates roundoff errors in computing Cauchy principal value integrals using standard adaptive quadratures, proposing a method that controls error tolerance and provides reliable error estimation. Numerical experiments show the method competes successfully with other algorithms.
We investigate the possibility of fast, accurate and reliable computation of the Cauchy principal value integrals $\mathrm{P}\!\int_{a}^{b} f(x)(x-τ)^{-1} dx$ $(a < τ< b)$ using standard adaptive quadratures. In order to properly control the error tolerance for the adaptive quadrature and to obtain a~reliable estimation of the approximation error, we research the possible influence of round-off errors on the computed result. As the numerical experiments confirm, the proposed method can successfully compete with other algorithms for computing such type integrals. Moreover, the presented method is very easy to implement on any system equipped with a reliable adaptive integration subroutine.