Minimization Stopping Parameters - GNU Scientific Library -- Reference Manual
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### 34.6 Stopping Parameters

A minimization procedure should stop when one of the following conditions is true:

- A minimum has been found to within the user-specified precision.
- A user-specified maximum number of iterations has been reached.
- An error has occurred.

The handling of these conditions is under user control. The function below allows the user to test the precision of the current result.

— Function: int gsl_min_test_interval (double x_lower, double x_upper, double epsabs, double epsrel)

> This function tests for the convergence of the interval [x_lower, x_upper] with absolute error epsabs and relative error epsrel. The test returns `GSL_SUCCESS` if the following condition is achieved,

>               |a - b| < epsabs + epsrel min(|a|,|b|)

> when the interval x = [a,b] does not include the origin. If the interval includes the origin then \min(|a|,|b|) is replaced by zero (which is the minimum value of |x| over the interval). This ensures that the relative error is accurately estimated for minima close to the origin.

> This condition on the interval also implies that any estimate of the minimum x_m in the interval satisfies the same condition with respect to the true minimum x_m^*,

>               |x_m - x_m^*| < epsabs + epsrel x_m^*

> assuming that the true minimum x_m^* is contained within the interval.

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