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<html>
<head>
<title>
JACOBI_EIGENVALUE - Eigenvalues and Eigenvectors of a Symmetric Matrix
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
JACOBI_EIGENVALUE <br> Eigenvalues and Eigenvectors of a Symmetric Matrix
</h1>
<hr>
<p>
<b>JACOBI_EIGENVALUE</b>
is a MATLAB library which
computes the eigenvalues and eigenvectors of a real symmetric matrix.
</p>
<p>
Given a real symmetric NxN matrix A, <b>JACOBI_EIGENVALUE</b> carries out
an iterative procedure known as Jacobi's iteration, to determine a
N-vector D of real, positive eigenvalues, and an NxN matrix V whose
columns are the corresponding eigenvectors, so that, for each column
J of the eigenmatrix:
<pre>
A * Vj = Dj * Vj
</pre>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files 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_EIGENVALUE</b> is available in
<a href = "../../c_src/jacobi_eigenvalue/jacobi_eigenvalue.html">a C version</a> and
<a href = "../../cpp_src/jacobi_eigenvalue/jacobi_eigenvalue.html">a C++ version</a> and
<a href = "../../f77_src/jacobi_eigenvalue/jacobi_eigenvalue.html">a FORTRAN77 version</a> and
<a href = "../../f_src/jacobi_eigenvalue/jacobi_eigenvalue.html">a FORTRAN90 version</a> and
<a href = "../../m_src/jacobi_eigenvalue/jacobi_eigenvalue.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/arpack/arpack.html">
ARPACK</a>,
a MATLAB library which
uses Arnoldi methods
to compute some eigenvalues and eigenvectors of matrices,
which may be very large.
</p>
<p>
<a href = "../../m_src/test_eigen/test_eigen.html">
TEST_EIGEN</a>,
a MATLAB library which
implements test matrices for eigenvalue analysis.
</p>
<p>
<a href = "../../m_src/test_mat/test_mat.html">
TEST_MAT</a>,
a MATLAB library which
defines test matrices, some of
which have known determinants, eigenvalues and eigenvectors,
inverses and so on.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Gene Golub, Charles VanLoan,<br>
Matrix Computations,
Third Edition,<br>
Johns Hopkins, 1996,<br>
ISBN: 0-8018-4513-X,<br>
LC: QA188.G65.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "jacobi_eigenvalue.m">jacobi_eigenvalue.m</a>,
computes the eigenvalues and eigenvectors of a real
symmetric matrix.
</li>
<li>
<a href = "r8mat_is_eigen_right.m">r8mat_is_eigen_right.m</a>,
determines the error in a (right) eigensystem.
</li>
<li>
<a href = "r8mat_norm_fro.m">r8mat_norm_fro.m</a>,
returns the Frobenius norm (square root of sum of squares) of a matrix.
</li>
<li>
<a href = "r8mat_print.m">r8mat_print.m</a>,
prints an R8MAT.
</li>
<li>
<a href = "r8mat_print_some.m">r8mat_print_some.m</a>,
prints some of an R8MAT.
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>,
prints an R8VEC.
</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_eigenvalue_test.m">jacobi_eigenvalue_test.m</a>,
calls all the tests.
</li>
<li>
<a href = "jacobi_eigenvalue_test_output.txt">jacobi_eigenvalue_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "jacobi_eigenvalue_test01.m">jacobi_eigenvalue_test01.m</a>,
tests a full 4x4 matrix.
</li>
<li>
<a href = "jacobi_eigenvalue_test02.m">jacobi_eigenvalue_test02.m</a>,
tests a diagonal 4x4 matrix.
</li>
<li>
<a href = "jacobi_eigenvalue_test03.m">jacobi_eigenvalue_test03.m</a>,
tests a tridiagonal 5x5 matrix.
</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 revised on 14 July 2013.
</i>
<!-- John Burkardt -->
</body>
</html>