Abstract
The aim of this paper is to tackle the numerical calculation of the so-called finite-part integrals, including Cauchy principal value integrals and any supersingular integral. The numerical procedure consists of replacing the density function f(t) by the polynomial that is the best fit in a least-squares sense for the values f(zk), where {zk} is a set of distinct points located on an ellipse that surrounds the interval [−1,1]. This method works in all mentioned cases, it does not depend on derivatives of f(t), and provides very accurate results when f is smooth enough. Some examples show the performance of this approach.
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