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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.

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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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