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What is the difference between AccuracyGoal and PrecisionGoal for NIntegrate function?
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AccuracyGoal effectively specifies the absolute error allowed in a numerical procedure.
An accuracy goal is one where we are motivated to arrive at the most accurate possible conclusion. These occur when the cost of being inaccurate is high. Unsurprisingly, people invest more effort in achieving accuracy goals, as any deviation costs, and a large deviation may well more.
I think this sentence from the Mma help system is almost enough:
With PrecisionGoal->p and AccuracyGoal->a, Mathematica attempts to make the numerical error in a result of size x be less than (10^-a)+Abs[x] 10^-p.
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