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Abstract
Partition-extrapolation methods for numerical quadratures are based on dividing the range of integration into an infinite number of subdomains, evaluating the subintegrals over a finite number of subdomains numerically, and then estimating the integral by extrapolation of the partial sums. There is considerable flexibility in the choice of subdivisions, method of evaluating the subintegrals and extrapolation procedure.
The treatment is heuristic, it being shown that the present methods compare favorably with previous methods for a variety of examples involving semi-infinite ranges or integrands with singularities.