PrecisionGoal
is an option for various numerical operations which specifies how many effective digits of precision should be sought in the final result.
Details
- PrecisionGoal is an option for such functions as NIntegrate and NDSolve.
- PrecisionGoal->Automatic normally yields a precision goal equal to half 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 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 PrecisionGoal->p and AccuracyGoal->a, the Wolfram Language attempts to make the numerical error in a result of size x be less than
![10^(-a)+TemplateBox[{x}, Abs]10^(-p)](Files/PrecisionGoal.en/1.png "10^(-a)+TemplateBox[{x}, Abs]10^(-p)")
.
Examples
open allclose allBasic Examples (2)
Approximate an integral to at least 10 digits of precision:
Use accuracy (absolute error) as the basis for error control in solving an ODE:
Without specifying the PrecisionGoal, the error is much larger:
Scope (2)
Find a minimum with convergence criteria 
and 
:
Try with convergence criteria 
and 
:
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:
Text
Wolfram Research (1991), PrecisionGoal, Wolfram Language function, https://reference.wolfram.com/language/ref/PrecisionGoal.html (updated 2003).
CMS
Wolfram Language. 1991. "PrecisionGoal." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/PrecisionGoal.html.
APA
Wolfram Language. (1991). PrecisionGoal. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PrecisionGoal.html