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Technology-enabling science of the computational universe. An integration strategy normally prescribes how to manage and create new elements of a set of disjoint subregions of the initial integral region. Each subregion might have its own integrand and integration rule associated with it.
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The integral estimate is the sum of the integral estimates of all subregions. Integration strategies use integration rules to compute the subregion integral estimates. To improve an integral estimate the integrand should be sampled at additional points. Both approaches can use symbolic preprocessing and variable transformation or sequence summation acceleration to achieve faster convergence.
Here is a plot of all sampling points used in the integration. The patterns formed by the sampling points at the upper part of the plot differ from the patterns of the lower part of the plot because a singularity handler is applied. Adaptive Strategies” gives a general description of the adaptive strategies. Complementary to it is the local adaptive strategy, which is explained in “Local Adaptive Strategy”.