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<h3 class="section">34.4 Iteration</h3>
<p>The following functions drive the iteration of each algorithm. Each
function performs one iteration to update the state of any solver of the
corresponding type. The same functions work for all solvers so that
different methods can be substituted at runtime without modifications to
the code.
<div class="defun">
— Function: int <b>gsl_multiroot_fsolver_iterate</b> (<var>gsl_multiroot_fsolver * s</var>)<var><a name="index-gsl_005fmultiroot_005ffsolver_005fiterate-2292"></a></var><br>
— Function: int <b>gsl_multiroot_fdfsolver_iterate</b> (<var>gsl_multiroot_fdfsolver * s</var>)<var><a name="index-gsl_005fmultiroot_005ffdfsolver_005fiterate-2293"></a></var><br>
<blockquote><p>These functions perform a single iteration of the solver <var>s</var>. If the
iteration encounters an unexpected problem then an error code will be
returned,
<dl>
<dt><code>GSL_EBADFUNC</code><dd>the iteration encountered a singular point where the function or its
derivative evaluated to <code>Inf</code> or <code>NaN</code>.
<br><dt><code>GSL_ENOPROG</code><dd>the iteration is not making any progress, preventing the algorithm from
continuing.
</dl>
</p></blockquote></div>
<p>The solver maintains a current best estimate of the root at all times.
This information can be accessed with the following auxiliary functions,
<div class="defun">
— Function: gsl_vector * <b>gsl_multiroot_fsolver_root</b> (<var>const gsl_multiroot_fsolver * s</var>)<var><a name="index-gsl_005fmultiroot_005ffsolver_005froot-2294"></a></var><br>
— Function: gsl_vector * <b>gsl_multiroot_fdfsolver_root</b> (<var>const gsl_multiroot_fdfsolver * s</var>)<var><a name="index-gsl_005fmultiroot_005ffdfsolver_005froot-2295"></a></var><br>
<blockquote><p>These functions return the current estimate of the root for the solver <var>s</var>.
</p></blockquote></div>
<div class="defun">
— Function: gsl_vector * <b>gsl_multiroot_fsolver_f</b> (<var>const gsl_multiroot_fsolver * s</var>)<var><a name="index-gsl_005fmultiroot_005ffsolver_005ff-2296"></a></var><br>
— Function: gsl_vector * <b>gsl_multiroot_fdfsolver_f</b> (<var>const gsl_multiroot_fdfsolver * s</var>)<var><a name="index-gsl_005fmultiroot_005ffdfsolver_005ff-2297"></a></var><br>
<blockquote><p>These functions return the function value f(x) at the current
estimate of the root for the solver <var>s</var>.
</p></blockquote></div>
<div class="defun">
— Function: gsl_vector * <b>gsl_multiroot_fsolver_dx</b> (<var>const gsl_multiroot_fsolver * s</var>)<var><a name="index-gsl_005fmultiroot_005ffsolver_005fdx-2298"></a></var><br>
— Function: gsl_vector * <b>gsl_multiroot_fdfsolver_dx</b> (<var>const gsl_multiroot_fdfsolver * s</var>)<var><a name="index-gsl_005fmultiroot_005ffdfsolver_005fdx-2299"></a></var><br>
<blockquote><p>These functions return the last step dx taken by the solver
<var>s</var>.
</p></blockquote></div>
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