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jacobi.html
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<html>
<head>
<title>
JACOBI - The Jacobi Iteration for Linear Systems
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
JACOBI <br> The Jacobi Iteration for Linear Systems
</h1>
<hr>
<p>
<b>JACOBI</b>
is a MATLAB library which
sets up the Jacobi 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>JACOBI</b> is available in
<a href = "../../c_src/jacobi/jacobi.html">a C version</a> and
<a href = "../../cpp_src/jacobi/jacobi.html">a C++ version</a> and
<a href = "../../f77_src/jacobi/jacobi.html">a FORTRAN77 version</a> and
<a href = "../../f_src/jacobi/jacobi.html">a FORTRAN90 version</a> and
<a href = "../../m_src/jacobi/jacobi.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/gauss_seidel.html">
GAUSS_SEIDEL</a>,
a MATLAB library which
implements the Gauss-Seidel iteration for linear systems.
</p>
<p>
<a href = "../../m_src/jacobi_poisson_1d/jacobi_poisson_1d.html">
JACOBI_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 Jacobi iteration.
</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>
<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 = "jacobi1.m">jacobi1.m</a>,
carries out one step of the Jacobi iteration.
</li>
<li>
<a href = "jacobi2.m">jacobi2.m</a>,
carries out one step of the Jacobi iteration, using
MATLAB's vector notation.
</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 = "jacobi_test.m">jacobi_test.m</a>, calls all the tests;
</li>
<li>
<a href = "jacobi_test_output.txt">jacobi_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "jacobi_test01.m">jacobi_test01.m</a>,
tests JACOBI1 on the -1,2,-1 matrix;
</li>
<li>
<a href = "jacobi_residual.png">jacobi_residual.png</a>
a PNG image of the square of the norm of the residual (Ax-b).
</li>
<li>
<a href = "jacobi_evolution.png">jacobi_evolution.png</a>
a PNG image of the evolution or trajectories of the solution values as the
iteration proceeds.
</li>
<li>
<a href = "jacobi_motion.png">jacobi_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 25 June 2011.
</i>
<!-- John Burkardt -->
</body>
</html>