# 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.
• 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 ndigit 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 , the Wolfram Language attempts to make the numerical error in a result of size be less than .

# Examples

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## Basic 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:

The relative error is small:

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:

Wolfram Research (1988), AccuracyGoal, Wolfram Language function, https://reference.wolfram.com/language/ref/AccuracyGoal.html (updated 2003).

#### 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

#### BibTeX

@misc{reference.wolfram_2024_accuracygoal, author="Wolfram Research", title="{AccuracyGoal}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/AccuracyGoal.html}", note=[Accessed: 13-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_accuracygoal, organization={Wolfram Research}, title={AccuracyGoal}, year={2003}, url={https://reference.wolfram.com/language/ref/AccuracyGoal.html}, note=[Accessed: 13-September-2024 ]}