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<a name="Overview-of-Sparse-Linear-Algebra"></a>
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<p>
Next: <a href="Sparse-Iterative-Solvers.html#Sparse-Iterative-Solvers" accesskey="n" rel="next">Sparse Iterative Solvers</a>, Up: <a href="Sparse-Linear-Algebra.html#Sparse-Linear-Algebra" accesskey="u" rel="up">Sparse Linear Algebra</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Overview-8"></a>
<h3 class="section">43.1 Overview</h3>
<a name="index-sparse-linear-algebra_002c-overview"></a>

<p>This chapter is primarily concerned with the solution of the
linear system
</p><div class="example">
<pre class="example">A x = b
</pre></div>
<p>where <em>A</em> is a general square <em>n</em>-by-<em>n</em> non-singular
sparse matrix, <em>x</em> is an unknown <em>n</em>-by-<em>1</em> vector, and
<em>b</em> is a given <em>n</em>-by-1 right hand side vector. There exist
many methods for solving such sparse linear systems, which broadly
fall into either direct or iterative categories. Direct methods include
LU and QR decompositions, while iterative methods start with an
initial guess for the vector <em>x</em> and update the guess through
iteration until convergence. GSL does not currently provide any
direct sparse solvers.
</p>



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