Error Distribution for Iterated Integrals
نویسندگان
چکیده
Abstract: In earlier work we demonstrated that iterated numerical integration outperforms ”standard” multivariate integration techniques for various function classes with singularities inside the domain of integration. We focus on the accuracy requirements to be applied in different directions or combinations of directions of iterated integrals. The integrals are approximated numerically in an ”automatic” (black-box) manner, where the user poses an accuracy requirement for the multivariate integral and expects a result within that tolerance. For an iterated integration it is generally accepted that an inner integral should be evaluated more accurately than its outer integrals in order to avoid the impression of roundoff error. We propose techniques for setting the error tolerances in different directionsi and give numerical results.
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