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<html>
<head>
<title>
GAUSS_SEIDEL - The Gauss Seidel Iteration for Linear Systems
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
GAUSS_SEIDEL <br> The Gauss Seidel Iteration for Linear Systems
</h1>
<hr>
<p>
<b>GAUSS_SEIDEL</b>
is a MATLAB library which
sets up the Gauss Seidel iteration for linear systems.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>GAUSS_SEIDEL</b> is available in
<a href = "../../m_src/gauss_seidel/gauss_seidel.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/cg_rc/cg_rc.html">
CG_RC</a>,
a MATLAB library which
implements the conjugate gradient method for solving
a positive definite sparse linear system A*x=b, using reverse communication.
</p>
<p>
<a href = "../../m_src/gauss_seidel_poisson_1d/gauss_seidel_poisson_1d.html">
GAUSS_SEIDEL_POISSON_1D</a>,
a MATLAB program which
demonstrates how the linear system for a discretized version of the
steady 1D Poisson equation can be solved by the Gauss-Seidel iteration.
</p>
<p>
<a href = "../../m_src/jacobi/jacobi.html">
JACOBI</a>,
a MATLAB library which
implements the Jacobi iteration for linear systems.
</p>
<p>
<a href = "../../m_src/sor/sor.html">
SOR</a>,
a MATLAB library which
implements a simple version of the successive over-relaxation (SOR)
method for the iteration solution of a linear system of equations.
</p>
<p>
<a href = "../../m_src/test_mat/test_mat.html">
TEST_MAT</a>,
a MATLAB library which
defines test matrices.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ul>
<li>
Tim Kelley,<br>
Iterative Methods for Linear and Nonlinear Equations,<br>
SIAM, 2004,<br>
ISBN: 0898713528,<br>
LC: QA297.8.K45.
</li>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "dif2.m">dif2.m</a>,
defines the -1, 2, -1 tridiagonal matrix.
</li>
<li>
<a href = "gauss_seidel1.m">gauss_seidel1.m</a>,
carries out one step of the Gauss Seidel iteration.
</li>
<li>
<a href = "gauss_seidel2.m">gauss_seidel2.m</a>,
carries out one step of the Gauss Seidel iteration,
assuming sparse matrix storage.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "gauss_seidel_test.m">gauss_seidel_test.m</a>, calls all the tests;
</li>
<li>
<a href = "gauss_seidel_test_output.txt">gauss_seidel_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "gauss_seidel_test01.m">gauss_seidel_test01.m</a>,
tests gauss_seidel1;
</li>
<li>
<a href = "gauss_seidel_test02.m">gauss_seidel_test02.m</a>,
tests gauss_seidel2;
</li>
<li>
<a href = "gauss_seidel_error.png">gauss_seidel_error.png</a>
a PNG image of the square of the norm of the residual (Ax-b).
</li>
<li>
<a href = "gauss_seidel_evolution.png">gauss_seidel_evolution.png</a>
a PNG image of the evolution or trajectories of the solution values as the
iteration proceeds.
</li>
<li>
<a href = "gauss_seidel_motion.png">gauss_seidel_motion.png</a>
a PNG image of the "motion" of the solution values, which is the averaged distance
each entry moves during an iteration.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last modified on 22 November 2011.
</i>
<!-- John Burkardt -->
</body>
</html>