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<title>GNU Scientific Library – Reference Manual: Search Stopping Parameters for the multidimensional solver</title>
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<a name="Search-Stopping-Parameters-for-the-multidimensional-solver"></a>
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<p>
Next: <a href="Algorithms-using-Derivatives.html#Algorithms-using-Derivatives" accesskey="n" rel="next">Algorithms using Derivatives</a>, Previous: <a href="Iteration-of-the-multidimensional-solver.html#Iteration-of-the-multidimensional-solver" accesskey="p" rel="previous">Iteration of the multidimensional solver</a>, Up: <a href="Multidimensional-Root_002dFinding.html#Multidimensional-Root_002dFinding" accesskey="u" rel="up">Multidimensional Root-Finding</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Search-Stopping-Parameters-2"></a>
<h3 class="section">36.5 Search Stopping Parameters</h3>
<a name="index-root-finding_002c-stopping-parameters-1"></a>
<p>A root finding procedure should stop when one of the following conditions is
true:
</p>
<ul>
<li> A multidimensional root has been found to within the user-specified precision.
</li><li> A user-specified maximum number of iterations has been reached.
</li><li> An error has occurred.
</li></ul>
<p>The handling of these conditions is under user control. The functions
below allow the user to test the precision of the current result in
several standard ways.
</p>
<dl>
<dt><a name="index-gsl_005fmultiroot_005ftest_005fdelta"></a>Function: <em>int</em> <strong>gsl_multiroot_test_delta</strong> <em>(const gsl_vector * <var>dx</var>, const gsl_vector * <var>x</var>, double <var>epsabs</var>, double <var>epsrel</var>)</em></dt>
<dd>
<p>This function tests for the convergence of the sequence by comparing the
last step <var>dx</var> with the absolute error <var>epsabs</var> and relative
error <var>epsrel</var> to the current position <var>x</var>. The test returns
<code>GSL_SUCCESS</code> if the following condition is achieved,
</p>
<div class="example">
<pre class="example">|dx_i| < epsabs + epsrel |x_i|
</pre></div>
<p>for each component of <var>x</var> and returns <code>GSL_CONTINUE</code> otherwise.
</p></dd></dl>
<a name="index-residual_002c-in-nonlinear-systems-of-equations"></a>
<dl>
<dt><a name="index-gsl_005fmultiroot_005ftest_005fresidual"></a>Function: <em>int</em> <strong>gsl_multiroot_test_residual</strong> <em>(const gsl_vector * <var>f</var>, double <var>epsabs</var>)</em></dt>
<dd><p>This function tests the residual value <var>f</var> against the absolute
error bound <var>epsabs</var>. The test returns <code>GSL_SUCCESS</code> if the
following condition is achieved,
</p>
<div class="example">
<pre class="example">\sum_i |f_i| < epsabs
</pre></div>
<p>and returns <code>GSL_CONTINUE</code> otherwise. This criterion is suitable
for situations where the precise location of the root, <em>x</em>, is
unimportant provided a value can be found where the residual is small
enough.
</p></dd></dl>
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