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<title>Search Stopping Parameters for Minimization Algorithms - GNU Scientific Library -- Reference Manual</title>
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<a name="Search-Stopping-Parameters-for-Minimization-Algorithms"></a>
Next: <a rel="next" accesskey="n" href="Minimization-Algorithms-using-Derivatives.html">Minimization Algorithms using Derivatives</a>,
Previous: <a rel="previous" accesskey="p" href="Iteration-of-the-Minimization-Algorithm.html">Iteration of the Minimization Algorithm</a>,
Up: <a rel="up" accesskey="u" href="Nonlinear-Least_002dSquares-Fitting.html">Nonlinear Least-Squares Fitting</a>
<hr>
</div>
<h3 class="section">37.5 Search Stopping Parameters</h3>
<p><a name="index-nonlinear-fitting_002c-stopping-parameters-2409"></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 functions
below allow the user to test the current estimate of the best-fit
parameters in several standard ways.
<div class="defun">
— Function: int <b>gsl_multifit_test_delta</b> (<var>const gsl_vector * dx, const gsl_vector * x, double epsabs, double epsrel</var>)<var><a name="index-gsl_005fmultifit_005ftest_005fdelta-2410"></a></var><br>
<blockquote>
<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,
<pre class="example"> |dx_i| < epsabs + epsrel |x_i|
</pre>
<p class="noindent">for each component of <var>x</var> and returns <code>GSL_CONTINUE</code> otherwise.
</p></blockquote></div>
<p><a name="index-residual_002c-in-nonlinear-systems-of-equations-2411"></a>
<div class="defun">
— Function: int <b>gsl_multifit_test_gradient</b> (<var>const gsl_vector * g, double epsabs</var>)<var><a name="index-gsl_005fmultifit_005ftest_005fgradient-2412"></a></var><br>
<blockquote><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,
<pre class="example"> \sum_i |g_i| < epsabs
</pre>
<p class="noindent">and returns <code>GSL_CONTINUE</code> otherwise. This criterion is suitable
for situations where the precise location of the minimum, x,
is unimportant provided a value can be found where the gradient is small
enough.
</p></blockquote></div>
<div class="defun">
— Function: int <b>gsl_multifit_gradient</b> (<var>const gsl_matrix * J, const gsl_vector * f, gsl_vector * g</var>)<var><a name="index-gsl_005fmultifit_005fgradient-2413"></a></var><br>
<blockquote><p>This function computes the gradient <var>g</var> of \Phi(x) = (1/2)
||F(x)||^2 from the Jacobian matrix J and the function values
<var>f</var>, using the formula g = J^T f.
</p></blockquote></div>
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