Nested quadrature rules for Cauchy principal value integrals (Q1123533)

Starting from ideas of \textit{G. Monegato} [Computing 29, 337-354 (1982; Zbl 0485.65017)] and \textit{P. Rabinowitz} [Math. Comput. 41, 63-78 (1983; Zbl 0545.65012)], the author builds new cubature formulae to numerically evaluate integrals of Cauchy type \(\int^{b}_{a}f(x)/(x-\lambda)dx\), \(-\infty <a<\lambda <b<\infty\) by estimating their error, too. An automatic globally adaptive integration scheme is obtained. Numerical examples are considered.