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cg_rc.html
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<html>
<head>
<title>
CG_RC - Conjugate Gradient Method with Reverse Communication
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CG_RC <br> Conjugate Gradient Method with Reverse Communication
</h1>
<hr>
<p>
<b>CG_RC</b>
is a MATLAB library which
implements the conjugate gradient (CG) method for solving
a positive definite sparse linear system A*x=b,
using reverse communication (RC).
</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>CG_RC</b> is available in
<a href = "../../c_src/cg_rc/cg_rc.html">a C version</a> and
<a href = "../../cpp_src/cg_rc/cg_rc.html">a C++ version</a> and
<a href = "../../f77_src/cg_rc/cg_rc.html">a FORTRAN77 version</a> and
<a href = "../../f_src/cg_rc/cg_rc.html">a FORTRAN90 version</a> and
<a href = "../../m_src/cg_rc/cg_rc.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/backtrack_binary_rc/backtrack_binary_rc.html">
BACKTRACK_BINARY_RC</a>,
a MATLAB library which
carries out a backtrack search for a set of binary decisions, using
reverse communication (RC).
</p>
<p>
<a href = "../../m_src/bisection_rc/bisection_rc.html">
BISECTION_RC</a>,
a MATLAB library which
seeks a solution to the equation F(X)=0 using bisection
within a user-supplied change of sign interval [A,B].
The procedure is written using reverse communication (RC).
</p>
<p>
<a href = "../../m_src/cg/cg.html">
CG</a>,
a MATLAB library which
implements a simple version of the conjugate gradient (CG) method
for solving a system of linear equations of the form A*x=b,
suitable for situations in which the matrix A is positive definite
(only real, positive eigenvalues) and symmetric.
</p>
<p>
<a href = "../../m_src/cg_distributed/cg_distributed.html">
CG_DISTRIBUTED</a>,
a MATLAB program which
implements a version of the Conjugate Gradient (CG) NAS Parallel Benchmark
using distributed memory.
</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/jacobi.html">
JACOBI</a>,
a MATLAB library which
implements the Jacobi iteration for solving symmetric positive definite
systems of linear equations.
</p>
<p>
<a href = "../../m_src/linplus/linplus.html">
LINPLUS</a>,
a MATLAB library which
carries out operations such as matrix-vector products, matrix factorization,
direct and iterative linear solves for matrices in a variety of formats,
including banded, border-banded, circulant, lower triangular, pentadiagonal,
sparse, symmetric, toeplitz, tridiagonal, upper triangular and vandermonde formats.
</p>
<p>
<a href = "../../m_src/mgmres/mgmres.html">
MGMRES</a>,
a MATLAB library which
applies the restarted GMRES algorithm to solve a sparse linear system.
</p>
<p>
<a href = "../../m_src/sor/sor.html">
SOR</a>,
a MATLAB library which
implements a simple version of the successive over-relaxation (SOR)
method for the iteration solution of a linear system of equations.
</p>
<p>
<a href = "../../m_src/sort_rc/sort_rc.html">
SORT_RC</a>,
a MATLAB library which
can sort a list of any kind of objects,
using reverse communication (RC).
</p>
<p>
<a href = "../../m_src/templates/templates.html">
TEMPLATES</a>,
a MATLAB library which
carries out simple versions of various iterative solvers.
</p>
<p>
<a href = "../../m_src/zero_rc/zero_rc.html">
ZERO_RC</a>,
a MATLAB 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>
Richard Barrett, Michael Berry, Tony Chan, James Demmel,
June Donato, Jack Dongarra, Victor Eijkhout, Roidan Pozo,
Charles Romine, Henk van der Vorst,<br>
Templates for the Solution of Linear Systems:
Building Blocks for Iterative Methods,<br>
SIAM, 1994,<br>
ISBN: 0898714710,<br>
LC: QA297.8.T45.
</li>
<li>
Jonathan Shewchuk,<br>
An introduction to the conjugate gradient method without the agonizing pain,
Edition 1.25, August 1994.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "cg_rc.m">cg_rc.m</a>
is a reverse communication conjugate gradient routine.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a time stamp.
</li>
<li>
<a href = "wathen.m">wathen.m</a>
returns the WATHEN matrix.
</li>
<li>
<a href = "wathen_order.m">wathen_order.m</a>
returns the order of the WATHEN matrix.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "cg_rc_test.m">cg_rc_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "cg_rc_test01.m">cg_rc_test01.m</a>,
uses the 1, -2, 1 matrix.
</li>
<li>
<a href = "cg_rc_test02.m">cg_rc_test02.m</a>,
uses the Wathen matrix.
</li>
<li>
<a href = "cg_rc_test_output.txt">cg_rc_test_output.txt</a>,
the output file.
</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 13 January 2013.
</i>
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