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<title>GNU Scientific Library – Reference Manual: Iterating the Sparse Linear System</title>
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<a name="Iterating-the-Sparse-Linear-System"></a>
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Previous: <a href="Sparse-Iterative-Solvers-Types.html#Sparse-Iterative-Solvers-Types" accesskey="p" rel="previous">Sparse Iterative Solvers Types</a>, Up: <a href="Sparse-Iterative-Solvers.html#Sparse-Iterative-Solvers" accesskey="u" rel="up">Sparse Iterative Solvers</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Iterating-the-Sparse-Linear-System-1"></a>
<h4 class="subsection">43.2.3 Iterating the Sparse Linear System</h4>
<p>The following functions are provided to allocate storage for the
sparse linear solvers and iterate the system to a solution.
</p>
<dl>
<dt><a name="index-gsl_005fsplinalg_005fitersolve_005falloc"></a>Function: <em>gsl_splinalg_itersolve *</em> <strong>gsl_splinalg_itersolve_alloc</strong> <em>(const gsl_splinalg_itersolve_type * <var>T</var>, const size_t <var>n</var>, const size_t <var>m</var>)</em></dt>
<dd><p>This function allocates a workspace for the iterative solution of
<var>n</var>-by-<var>n</var> sparse matrix systems. The iterative solver type
is specified by <var>T</var>. The argument <var>m</var> specifies the size
of the solution candidate subspace <em>{\cal K}_m</em>. The dimension
<var>m</var> may be set to 0 in which case a reasonable default value is used.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsplinalg_005fitersolve_005ffree"></a>Function: <em>void</em> <strong>gsl_splinalg_itersolve_free</strong> <em>(gsl_splinalg_itersolve * <var>w</var>)</em></dt>
<dd><p>This function frees the memory associated with the workspace <var>w</var>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsplinalg_005fitersolve_005fname"></a>Function: <em>const char *</em> <strong>gsl_splinalg_itersolve_name</strong> <em>(const gsl_splinalg_itersolve * <var>w</var>)</em></dt>
<dd><p>This function returns a string pointer to the name of the solver.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsplinalg_005fitersolve_005fiterate"></a>Function: <em>int</em> <strong>gsl_splinalg_itersolve_iterate</strong> <em>(const gsl_spmatrix *<var>A</var>, const gsl_vector *<var>b</var>, const double <var>tol</var>, gsl_vector *<var>x</var>, gsl_splinalg_itersolve *<var>w</var>)</em></dt>
<dd><p>This function performs one iteration of the iterative method for
the sparse linear system specfied by the matrix <var>A</var>, right hand
side vector <var>b</var> and solution vector <var>x</var>. On input, <var>x</var>
must be set to an initial guess for the solution. On output,
<var>x</var> is updated to give the current solution estimate. The
parameter <var>tol</var> specifies the relative tolerance between the residual
norm and norm of <var>b</var> in order to check for convergence.
When the following condition is satisfied:
</p><div class="example">
<pre class="example">|| A x - b || <= tol * || b ||
</pre></div>
<p>the method has converged, the function returns <code>GSL_SUCCESS</code> and
the final solution is provided in <var>x</var>. Otherwise, the function
returns <code>GSL_CONTINUE</code> to signal that more iterations are
required. Here, <em>|| \cdot ||</em> represents the Euclidean norm.
The input matrix <var>A</var> may be in triplet or compressed column
format.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fsplinalg_005fitersolve_005fnormr"></a>Function: <em>double</em> <strong>gsl_splinalg_itersolve_normr</strong> <em>(const gsl_splinalg_itersolve *<var>w</var>)</em></dt>
<dd><p>This function returns the current residual norm
<em>||r|| = ||A x - b||</em>, which is updated after each call to
<code>gsl_splinalg_itersolve_iterate</code>.
</p></dd></dl>
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