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

# Examples

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## Basic 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:

The error is small:

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:

Wolfram Research (1991), PrecisionGoal, Wolfram Language function, https://reference.wolfram.com/language/ref/PrecisionGoal.html (updated 2003).

#### 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

#### BibTeX

@misc{reference.wolfram_2024_precisiongoal, author="Wolfram Research", title="{PrecisionGoal}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/PrecisionGoal.html}", note=[Accessed: 12-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_precisiongoal, organization={Wolfram Research}, title={PrecisionGoal}, year={2003}, url={https://reference.wolfram.com/language/ref/PrecisionGoal.html}, note=[Accessed: 12-August-2024 ]}