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<html>
<head>
<title>
BISECTION_RC - Nonlinear Equation Solver Using Bisection, with Reverse Communication
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BISECTION_RC <br> Nonlinear Equation Solver Using Bisection, with Reverse Communication
</h1>
<hr>
<p>
<b>BISECTION_RC</b>
is a C++ library which
demonstrates the simple bisection method for solving a scalar nonlinear
equation in a change of sign interval, using reverse communication (RC).
</p>
<p>
The routine assumes that an interval [a,b] is known, over which
the function f(x) is continuous, and for which f(a)
and f(b) are of opposite sign. By repeatedly computing and testing
the midpoint, the halving change of sign interval may be reduced,
so that either the uncertainty interval or the magnitude of the function value
becomes small enough to satisfy the user as an approximation to the
location of a root of the function.
</p>
<p>
This routine is in part a demonstration of the idea of reverse communication.
Many zero finders require that the user define f(x) by writing a function
with a very specific set of input and output arguments, and sometimes with
a specific name, so that the user can call the zero finder, which in turn
can call the function. This is sometimes an awkward formulation to follow.
Reverse communication instead allows the user's calling program to retain
control of the function evaluation.
</p>
<p>
To use the reverse communication zero finder, the user defines the values
of A and B, and sets a parameter JOB to zero to indicate that this is the
first call. From then on, the zero finder repeatedly returns a value X,
asking the user to evaluate the function there. Once the user has evaluated
FX = f(X), the user may accept this approximation to the root, or else
call the zero finder again, passing the just-computed value of FX so that it
can take another bisection step.
</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>BISECTION_RC</b> is available in
<a href = "../../c_src/bisection_rc/bisection_rc.html">a C version</a> and
<a href = "../../cpp_src/bisection_rc/bisection_rc.html">a C++ version</a> and
<a href = "../../f77_src/bisection_rc/bisection_rc.html">a FORTRAN77 version</a> and
<a href = "../../f_src/bisection_rc/bisection_rc.html">a FORTRAN90 version</a> and
<a href = "../../m_src/bisection_rc/bisection_rc.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/backtrack_binary_rc/backtrack_binary_rc.html">
BACKTRACK_BINARY_RC</a>,
a C++ library which
carries out a backtrack search for a set of binary decisions, using
reverse communication (RC).
</p>
<p>
<a href = "../../cpp_src/bisection_integer/bisection_integer.html">
BISECTION_INTEGER</a>,
a C++ library which
seeks an integer solution to the equation F(X)=0,
using bisection within a user-supplied change of sign interval [A,B].
</p>
<p>
<a href = "../../cpp_src/brent/brent.html">
BRENT</a>,
a C++ library which
contains Richard Brent's routines for finding the zero, local minimizer,
or global minimizer of a scalar function of a scalar argument, without
the use of derivative information.
</p>
<p>
<a href = "../../cpp_src/cg_rc/cg_rc.html">
CG_RC</a>,
a C++ library which
implements the conjugate gradient method for solving
a positive definite sparse linear system A*x=b,
using reverse communication (RC).
</p>
<p>
<a href = "../../cpp_src/sort_rc/sort_rc.html">
SORT_RC</a>,
a C++ library which
can sort a list of any kind of objects,
using reverse communication (RC).
</p>
<p>
<a href = "../../cpp_src/test_zero/test_zero.html">
TEST_ZERO</a>,
a C++ library which
implements test problems for the solution
of a single nonlinear equation in one variable.
</p>
<p>
<a href = "../../cpp_src/zero_rc/zero_rc.html">
ZERO_RC</a>,
a C++ library which
seeks solutions of a scalar nonlinear equation f(x) = 0,
or a system of nonlinear equations,
using reverse communication (RC).
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Werner Rheinboldt,<br>
Algorithms for finding zeros of a function,<br>
UMAP Journal,<br>
Volume 2, Number 1, 1981, pages 43-72.
</li>
<li>
Werner Rheinboldt,<br>
Methods for Solving Systems of Nonlinear Equations,<br>
SIAM, 1998,<br>
ISBN: 089871415X,<br>
LC: QA214.R44.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "bisection_rc.cpp">bisection_rc.cpp</a>, the source code.
</li>
<li>
<a href = "bisection_rc.hpp">bisection_rc.hpp</a>, the include file.
</li>
<li>
<a href = "bisection_rc.sh">bisection_rc.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "bisection_rc_prb.cpp">bisection_rc_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "bisection_rc_prb.sh">bisection_rc_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "bisection_rc_prb_output.txt">bisection_rc_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BISECTION_RC</b> seeks a zero of f(x) in a change of sign interval.
</li>
<li>
<b>R8_SIGN</b> returns the sign of an R8.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 14 January 2013.
</i>
<!-- John Burkardt -->
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