I found the documentation of wolfram appears to be written hurriedly since it seems to contain a number of unclear statements, e.g., equation numbers were often missed, texts in codes and those in corresponding results were often more or less inconsistent. Apart from such obvious errors, the expressions are sometimes ambiguous. For example, this is a snapshot from NIntegrate Integration Strategies

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  1. The integral values of all points: should it be the integrand values of all points?

  2. "GlobalAdaptive" has the ability to reuse very few integral values (...): does it mean that "GlobalAdaptive" can only reuse very few integrand values evaluated at the previous sampling point because it is an adaptive sampling scheme? Or it means the integral values of previous subintervals?

  3. $0$ for the default one-dimensional rule, the Gauss-Kronrod rule: in my understanding, the sampling points (or abscissas) in the default Gauss-Kronrod rule are fixed. Well, this sentence appears to imply that the sampling points of the Gauss-Kronrod rule are changing between samplings.

Can anyone help with understanding these?


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