This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# AccuracyGoal

 AccuracyGoalis 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 be less than .
Approximate a numerical integral to at least 8 digits of accuracy:
Use precision (relative error) as the basis for error control in solving an ODE:
The relative error is small:
Without specifying the AccuracyGoal, the relative error is much larger:
Approximate a numerical integral to at least 8 digits of accuracy:
 Out[1]=

Use precision (relative error) as the basis for error control in solving an ODE:
 Out[1]=
The relative error is small:
 Out[3]=
Without specifying the AccuracyGoal, the relative error is much larger:
 Out[4]=
 Scope   (2)
Find a minimum with convergence criteria and :
Use convergence criteria and :
Use convergence criteria and not possible at machine precision:
Use a higher working precision to allow convergence:
Solve a differential equation using high-precision arithmetic:
Use AccuracyGoal and PrecisionGoal at half the 32-digit working precision:
This corresponds to the automatic setting used by NDSolve: