BUILT-IN MATHEMATICA SYMBOL

# AccuracyGoal

AccuracyGoal
is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result.

## DetailsDetails

• AccuracyGoal is an option for such functions as NIntegrate, NDSolve, and FindRoot.
• normally yields an accuracy goal equal to half the setting for WorkingPrecision.
• 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.
• In most cases, you must set WorkingPrecision to be at least as large as AccuracyGoal.
• AccuracyGoal effectively specifies the absolute error allowed in a numerical procedure.
• With AccuracyGoal->a and , Mathematica attempts to make the numerical error in a result of size be less than .

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

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]=