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  • PrecisionGoal is an option for various numerical operations which specifies how many digits of precision should be sought in the final result.
  • PrecisionGoal is an option for such functions as NIntegrate and NDSolve.
  • PrecisionGoal -> Automatic yields a precision goal equal to 10 digits less than the setting for WorkingPrecision.
  • PrecisionGoal -> Infinity specifies that precision should not be used as the criterion for terminating the numerical procedure. AccuracyGoal is typically used in this case.
  • Even though you may specify PrecisionGoal-> n, the results you get may have much less than n-digit precision.
  • In most cases, you must set WorkingPrecision to be at least as large as PrecisionGoal.
  • PrecisionGoal effectively specifies the relative error allowed in a numerical procedure.
  • With PrecisionGoal-> p and AccuracyGoal-> a Mathematica attempts to make the numerical error in a result of size be less than .
  • See the Mathematica book: Section 3.9.3.
  • See also: AccuracyGoal, WorkingPrecision.