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PrecisionGoal

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

MORE INFORMATION

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, Mathematica attempts to make the numerical error in a result of size x be less than .

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:

AccuracyGoal WorkingPrecision Precision SetPrecision Accuracy

Numerical Integration

Controlling the Precision of Results

The Uncertainties of Numerical Mathematics

Differential Equations

Numerical Evaluation & Precision

Precision & Accuracy Control

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