AccuracyGoal
is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result.
Details
- AccuracyGoal is an option for such functions as NIntegrate, NDSolve, and FindRoot.
- AccuracyGoal->Automatic normally yields an accuracy goal equal to half the setting for WorkingPrecision.
- 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.
- 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 PrecisionGoal->p, the Wolfram Language attempts to make the numerical error in a result of size
be less than 
.
Examples
open allclose allBasic Examples (2)
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:
Without specifying the AccuracyGoal, the relative error is much larger:
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:
Text
Wolfram Research (1988), AccuracyGoal, Wolfram Language function, https://reference.wolfram.com/language/ref/AccuracyGoal.html (updated 2003).
CMS
Wolfram Language. 1988. "AccuracyGoal." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/AccuracyGoal.html.
APA
Wolfram Language. (1988). AccuracyGoal. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AccuracyGoal.html