Subdivision Logic
"Local" adaptive quadrature makes the acceptable error for a given interval proportional to the length of that interval. This criterion can be difficult to satisfy if the integrand are badly behaved at only a few points, for example with a few step discontinuities. Alternatively, one could require only that the sum of the errors on each of the subintervals be less than the user's requirement. This would be "global" adaptive quadrature. Global adaptive quadrature can be more efficient (using fewer evaluations of the integrand) but are generally more complex to program and may require more working space to record information on the current set of intervals.
Read more about this topic: Adaptive Quadrature
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