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<title>GNU Scientific Library – Reference Manual: Search Stopping Parameters for Minimization Algorithms</title>
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<a name="Search-Stopping-Parameters-for-Minimization-Algorithms"></a>
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<p>
Next: <a href="High-Level-Driver.html#High-Level-Driver" accesskey="n" rel="next">High Level Driver</a>, Previous: <a href="Iteration-of-the-Minimization-Algorithm.html#Iteration-of-the-Minimization-Algorithm" accesskey="p" rel="previous">Iteration of the Minimization Algorithm</a>, Up: <a href="Nonlinear-Least_002dSquares-Fitting.html#Nonlinear-Least_002dSquares-Fitting" accesskey="u" rel="up">Nonlinear Least-Squares Fitting</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Search-Stopping-Parameters-3"></a>
<h3 class="section">38.6 Search Stopping Parameters</h3>
<a name="index-nonlinear-fitting_002c-stopping-parameters"></a>
<p>A minimization procedure should stop when one of the following conditions is
true:
</p>
<ul>
<li> A minimum 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 current estimate of the best-fit
parameters in several standard ways.
</p>
<dl>
<dt><a name="index-gsl_005fmultifit_005ftest_005fdelta"></a>Function: <em>int</em> <strong>gsl_multifit_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,
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-1"></a>
<dl>
<dt><a name="index-gsl_005fmultifit_005ftest_005fgradient"></a>Function: <em>int</em> <strong>gsl_multifit_test_gradient</strong> <em>(const gsl_vector * <var>g</var>, double <var>epsabs</var>)</em></dt>
<dd><p>This function tests the residual gradient <var>g</var> against the absolute
error bound <var>epsabs</var>. Mathematically, the gradient should be
exactly zero at the minimum. The test returns <code>GSL_SUCCESS</code> if the
following condition is achieved,
and returns <code>GSL_CONTINUE</code> otherwise. This criterion is suitable
for situations where the precise location of the minimum, <em>x</em>,
is unimportant provided a value can be found where the gradient is small
enough.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fmultifit_005fgradient"></a>Function: <em>int</em> <strong>gsl_multifit_gradient</strong> <em>(const gsl_matrix * <var>J</var>, const gsl_vector * <var>f</var>, gsl_vector * <var>g</var>)</em></dt>
<dd><p>This function computes the gradient <var>g</var> of <em>\Phi(x) = (1/2)
||F(x)||^2</em> from the Jacobian matrix <em>J</em> and the function values
<var>f</var>, using the formula <em>g = J^T f</em>.
</p></dd></dl>
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