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AccuracyGoal

AccuracyGoal
is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result.
  • AccuracyGoal->Infinity specifies that accuracy should not be used as the criterion for terminating the numerical procedure. PrecisionGoal is typically used in this case.
  • Even though you may specify AccuracyGoal->n, the results you get may sometimes have much less than n-digit accuracy.
  • AccuracyGoal effectively specifies the absolute error allowed in a numerical procedure.
  • With AccuracyGoal->a and PrecisionGoal->p, Mathematica attempts to make the numerical error in a result of size x be less than 10^(-a)+❘x❘10^(-p).
Approximate a numerical integral to at least 8 digits of accuracy:
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Use precision (relative error) as the basis for error control in solving an ODE:
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The relative error is small:
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Without specifying the AccuracyGoal, the relative error is much larger:
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