BUILT-IN MATHEMATICA SYMBOL

# PrecisionGoal

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

## DetailsDetails

• PrecisionGoal is an option for such functions as NIntegrate and NDSolve.
• normally yields a precision goal equal to half the setting for WorkingPrecision.
• 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 , the results you get may sometimes 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 and AccuracyGoal->a, Mathematica attempts to make the numerical error in a result of size x be less than .

## ExamplesExamplesopen allclose all

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

Approximate an integral to at least 10 digits of precision:

 Out[1]=

Use accuracy (absolute error) as the basis for error control in solving an ODE:

 Out[1]=

The error is small:

 Out[3]=

Without specifying the PrecisionGoal, the error is much larger:

 Out[4]=