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<title>Minimization Stopping Parameters - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">33.6 Stopping Parameters</h3>
<p><a name="index-minimization_002c-stopping-parameters-2269"></a>
A minimization procedure should stop when one of the following
conditions is true:
<ul>
<li>A minimum has been found to within the user-specified precision.
<li>A user-specified maximum number of iterations has been reached.
<li>An error has occurred.
</ul>
<p class="noindent">The handling of these conditions is under user control. The function
below allows the user to test the precision of the current result.
<div class="defun">
— Function: int <b>gsl_min_test_interval</b> (<var>double x_lower, double x_upper, double epsabs, double epsrel</var>)<var><a name="index-gsl_005fmin_005ftest_005finterval-2270"></a></var><br>
<blockquote><p>This function tests for the convergence of the interval [<var>x_lower</var>,
<var>x_upper</var>] with absolute error <var>epsabs</var> and relative error
<var>epsrel</var>. The test returns <code>GSL_SUCCESS</code> if the following
condition is achieved,
<pre class="example"> |a - b| < epsabs + epsrel min(|a|,|b|)
</pre>
<p class="noindent">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.
<p>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^*,
<pre class="example"> |x_m - x_m^*| < epsabs + epsrel x_m^*
</pre>
<p class="noindent">assuming that the true minimum x_m^* is contained within the interval.
</p></blockquote></div>
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