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continuation.html
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<html>
<head>
<title>
CONTINUATION - A Sample 2D Continuation Code
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
CONTINUATION <br> A Sample 2D Continuation Code
</h1>
<hr>
<p>
<b>CONTINUATION</b>
is a MATLAB library which
implements the continuation method for a simple 2D problem,
which involves finding a point on the unit circle, and then
finding a sequence of nearby points which trace out the full
curve, using only the information available in the implicit
definition of the curve from the function f(x,y)=x^2+y^2-1.
</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>CONTINUATION</b> is available in
<a href = "../../m_src/continuation/continuation.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f77_src/pitcon66/pitcon66.html">
PITCON66</a>,
a FORTRAN77 library which
seeks to produce a sequence of points that satisfy a set of nonlinear
equations with one degree of freedom;
this is version 6.6 of ACM TOMS algorithm 596.
</p>
<p>
<a href = "../../f_src/pitcon7/pitcon7.html">
PITCON7</a>,
a FORTRAN90 library which
seeks to produce a sequence of points that satisfy a set of nonlinear
equations with one degree of freedom;
this is version 7.0 of ACM TOMS algorithm 596.
</p>
<p>
<a href = "../../m_src/test_con/test_con.html">
TEST_CON</a>,
a MATLAB library which
implements test problems for numerical continuation.
</p>
<p>
<a href = "../../f77_src/toms502/toms502.html">
TOMS502</a>,
a FORTRAN77 library which
seeks to produce a sequence of points that satisfy a set of nonlinear
equations with one degree of freedom;
this library is commonly called <b>DERPAR</b>;<br>
this is ACM TOMS algorithm 502.
</p>
<p>
<a href = "../../f77_src/toms596/toms596.html">
TOMS596</a>,
a FORTRAN77 library which
seeks to produce a sequence of points that satisfy a set of nonlinear
equations with one degree of freedom;
this library is commonly called <b>PITCON</b>;<br>
this is ACM TOMS algorithm 596.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Cor den Heijer, Werner Rheinboldt,<br>
On Steplength Algorithms for a Class of Continuation Methods,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 18, Number 5, October 1981, pages 925-947.
</li>
<li>
Werner Rheinboldt,<br>
Solution Field of Nonlinear Equations and Continuation Methods,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 17, Number 2, April 1980, pages 221-237.
</li>
<li>
Werner Rheinboldt,<br>
Numerical Analysis of Continuation Methods for Nonlinear
Structural Problems,<br>
Computers and Structures,<br>
Volume 13, 1981, pages 103-114.
</li>
<li>
Werner Rheinboldt, John Burkardt,<br>
A Locally Parameterized Continuation Process,<br>
ACM Transactions on Mathematical Software,<br>
Volume 9, Number 2, June 1983, pages 215-235.
</li>
<li>
Werner Rheinboldt, John Burkardt,<br>
Algorithm 596:
A Program for a Locally Parameterized
Continuation Process,<br>
ACM Transactions on Mathematical Software,<br>
Volume 9, Number 2, June 1983, pages 236-241.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "newton.m">newton.m</a>,
uses Newton's method to solve the augmented nonlinear system.
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>,
prints an R8VEC.
</li>
<li>
<a href = "step.m">step.m</a>,
takes one continuation step.
</li>
<li>
<a href = "tangent.m">tangent.m</a>,
computes the tangent vector.
</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 = "continuation_test.m">continuation_test.m</a>,
calls all the tests;
</li>
<li>
<a href = "continuation_test_output.txt">continuation_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "circle_test.m">circle_test.m</a>,
demonstrates the continuation method for finding points on a circle.
</li>
<li>
<a href = "circle_test.png">circle_test.png</a>,
a PNG image of the points computed on the circle.
</li>
<li>
<a href = "f_circle.m">f_circle.m</a>,
evaluates the function that implicitly defines a circle.
</li>
<li>
<a href = "fp_circle.m">fp_circle.m</a>,
evaluates the jacobian of the function that implicitly defines a circle.
<li>
<a href = "newton_test.m">newton_test.m</a>,
demonstrates the Newton code.
</li>
<li>
<a href = "step_test.m">step_test.m</a>,
demonstrates the continuation step code.
</li>
<li>
<a href = "tangent_test.m">tangent_test.m</a>,
demonstrates the tangent code.
</li>
</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 08 April 2014.
</i>
<!-- John Burkardt -->
</body>
</html>