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power_method.html
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<html>
<head>
<title>
POWER_METHOD - The Power Method for Eigenvalues and Eigenvectors
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
POWER_METHOD <br> The Power Method for Eigenvalues and Eigenvectors
</h1>
<hr>
<p>
<b>POWER_METHOD</b>
is a FORTRAN90 library which
carries out the power method.
</p>
<p>
The power method implemented here is given a real square matrix, and seeks
to determine the eigenvalue of maximum modulus, and a corresponding eigenvector.
</p>
<p>
The basic power method will not perform as expected if, corresponding to the
maximum modulus, there are complex eigenvalues, or a pair of real eigenvalues
of opposite sign. The power method's behavior can break down or be very
slow initially if the starting vector has a zero or very small component
in the eigenspace corresponding to the maximal eigenvalue.
</p>
<p>
A second version of the power method is included which can handle the case
of complex eigenvalues.
</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>POWER_METHOD</b> is available in
<a href = "../../c_src/power_method/power_method.html">a C version</a> and
<a href = "../../cpp_src/power_method/power_method.html">a C++ version</a> and
<a href = "../../f77_src/power_method/power_method.html">a FORTRAN77 version</a> and
<a href = "../../f_src/power_method/power_method.html">a FORTRAN90 version</a> and
<a href = "../../m_src/power_method/power_method.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/arpack/arpack.html">
ARPACK</a>,
a FORTRAN90 library which
computes eigenvalues for large matrices;
</p>
<p>
<a href = "../../f_src/eispack/eispack.html">
EISPACK</a>
a FORTRAN90 library which
carries out eigenvalue computations;
superseded by LAPACK;
</p>
<p>
<a href = "../../f_src/test_eigen/test_eigen.html">
TEST_EIGEN</a>,
a FORTRAN90 library which
implements test matrices for eigenvalue analysis.
</p>
<p>
<a href = "../../f_src/test_mat/test_mat.html">
TEST_MAT</a>,
a FORTRAN90 library which
defines test matrices.
</p>
<p>
<a href = "../../f77_src/toms343/toms343.html">
TOMS343</a>,
a FORTRAN77 library which
computes the eigenvalues and
eigenvectors of a general real matrix;<br>
this is a FORTRAN77 version of ACM TOMS algorithm 343.
</p>
<p>
<a href = "../../f77_src/toms384/toms384.html">
TOMS384</a>,
a FORTRAN77 library which
computes the eigenvalues and eigenvectors
of a symmetric matrix;<br>
this is a FORTRAN77 version of ACM TOMS algorithm 384.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Richard Burden, Douglas Faires,<br>
Numerical Analysis,<br>
Thomson Brooks/Cole, 2004,<br>
ISBN13: 978-0534392000,<br>
LC: QA297.B84.
</li>
<li>
Ward Cheney, David Kincaid,<br>
Numerical Mathematics and Computing,<br>
Brooks-Cole Publishing, 2004,<br>
ISBN: 0534201121,<br>
LC: QA297.C426.
</li>
<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>
<li>
Eric VanDeVelde,<br>
Concurrent Scientific Programming,<br>
Springer, 1994,<br>
ISBN: 0-387-94195-9,<br>
LC: QA76.58.V35.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "power_method.f90">power_method.f90</a>,
the source code.
</li>
<li>
<a href = "power_method.sh">power_method.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "power_method_prb.f90">power_method_prb.f90</a>, the tests;
</li>
<li>
<a href = "power_method_prb.sh">power_method_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "power_method_prb_output.txt">power_method_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>FIBONACCI2</b> returns the FIBONACCI2 matrix.
</li>
<li>
<b>POWER_METHOD</b> applies several steps of the power method.
</li>
<li>
<b>POWER_METHOD2</b> applies several steps of the power method.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIS</b> returns the TRIS matrix.
</li>
<li>
<b>TRIS_EIGENVALUES</b> returns the eigenvalues of the TRIS matrix.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last modified on 26 May 2008.
</i>
<!-- John Burkardt -->
</body>
</html>