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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.