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mgmres.html
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<html>
<head>
<title>
MGMRES - Restarted GMRES solver for sparse linear systems
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MGMRES <br> Restarted GMRES solver for sparse linear systems
</h1>
<hr>
<p>
<b>MGMRES</b>
is a C++ library which
applies the restarted Generalized Minimum Residual (GMRES) algorithm
to solve a sparse linear system, using compressed row (CR) or
sparse triplet (ST) format, by Lili Ju.
</p>
<p>
One matrix format used is the <b>ST</b> or "sparse triplet" format,
which sets <b>NZ_NUM</b> to the number of
nonzeros, and stores the K-th nonzero matrix entry as:
<ul>
<li>
<b>A(K)</b>, the value of the entry;
</li>
<li>
<b>IA(K)</b>, the row of the entry;
</li>
<li>
<b>JA(K)</b>, the column of the entry;
</li>
</ul>
</p>
<p>
Another matrix format used is the <b>CR</b> or
"sparse compressed row" format, which is similar to the sparse
triplet format except that it the vector of row indices is
compressed to a vector of length N+1 which points to the beginning
of the set of entries for each row.
<ul>
<li>
<b>A(1:NZ_NUM)</b>, the value of the entry;
</li>
<li>
<b>IA(1:N+1)</b>, row I values occur in entries IA(I) to IA(I+1)-1;
</li>
<li>
<b>JA(1:NZ_NUM)</b>, the column of the entry;
</li>
</ul>
</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>MGMRES</b> is available in
<a href = "../../c_src/mgmres/mgmres.html">a C version</a> and
<a href = "../../cpp_src/mgmres/mgmres.html">a C++ version</a> and
<a href = "../../f77_src/mgmres/mgmres.html">a FORTRAN77 version</a> and
<a href = "../../f_src/mgmres/mgmres.html">a FORTRAN90 version</a> and
<a href = "../../m_src/mgmres/mgmres.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../data/cc/cc.html">
CC</a>,
a data directory which
contains examples of the Compressed Column (CC)
sparse matrix file format;
</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.
</p>
<p>
<a href = "../../data/cr/cr.html">
CR</a>,
a data directory which
contains examples of the Compressed Row (CR)
sparse matrix file format;
</p>
<p>
<a href = "../../c_src/csparse/csparse.html">
CSPARSE</a>,
a C library which
implements iterative methods for solving linear systems.
</p>
<p>
<a href = "../../cpp_src/fem2d_poisson_sparse/fem2d_poisson_sparse.html">
FEM2D_POISSON_SPARSE</a>,
a C++ program which
solves the steady Poisson equation on a 2D triangulated region. The
program uses a copy of <b>MGMRES</b> to solve the linear system.
</p>
<p>
<a href = "../../datasets/hbsmc/hbsmc.html">
HBSMC</a>,
a dataset directory which
contains a collection of large sparse matrices stored in the
Harwell-Boeing format.
</p>
<p>
<a href = "../../cpp_src/linpack/linpack.html">
LINPACK</a>,
a C++ library
which carries out direct methods for solving linear systems.
</p>
<p>
<a href = "../../data/mm/mm.html">
MM</a>,
a data directory which
contains a description and examples of the Matrix Market format
for storing matrices.
</p>
<p>
<a href = "../../data/st/st.html">
ST</a>,
a data directory which
contains a description and examples of the ST format for storing sparse
matrices, which are used by the C and C++ versions of MGMRES.
</p>
<p>
<a href = "../../cpp_src/superlu/superlu.html">
SUPERLU</a>,
C++ programs which
illustrate how a C++ program can call the SUPERLU library,
(which is written in C),
which applies a fast direct solution method to solve
sparse linear systems,
by James Demmel, John Gilbert, and Xiaoye Li.
</p>
<p>
<a href = "../../cpp_src/test_mat/test_mat.html">
TEST_MAT</a>,
a C++ library which
defines test matrices.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Original C version by Lili Ju, Mathematics Department,
University of South Carolina;
C++ version by John Burkardt.
</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:<br>
Building Blocks for Iterative Methods,<br>
SIAM, 1994,<br>
ISBN: 0898714710,<br>
LC: QA297.8.T45.
</li>
<li>
Tim Kelley,<br>
Iterative Methods for Linear and Nonlinear Equations,<br>
SIAM, 2004,<br>
ISBN: 0898713528,<br>
LC: QA297.8.K45.
</li>
<li>
Yousef Saad,<br>
Iterative Methods for Sparse Linear Systems,<br>
Second Edition,<br>
SIAM, 20003,<br>
ISBN: 0898715342,<br>
LC: QA188.S17.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "mgmres.cpp">mgmres.cpp</a>, the source code.
</li>
<li>
<a href = "mgmres.hpp">mgmres.hpp</a>, the include file.
</li>
<li>
<a href = "mgmres.sh">mgmres.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "mgmres_prb.cpp">mgmres_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "mgmres_prb.sh">mgmres_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "mgmres_prb_output.txt">mgmres_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ATX_CR</b> computes A'*x for a matrix stored in sparse compressed row form.
</li>
<li>
<b>ATX_ST</b> computes A'*x for a matrix stored in sparse triplet form.
</li>
<li>
<b>AX_CR</b> computes A*x for a matrix stored in sparse compressed row form.
</li>
<li>
<b>AX_ST</b> computes A*x for a matrix stored in sparse triplet form.
</li>
<li>
<b>DIAGONAL_POINTER_CR</b> finds diagonal entries in a sparse compressed row matrix.
</li>
<li>
<b>ILU_CR</b> computes the incomplete LU factorization of a matrix.
</li>
<li>
<b>LUS_CR</b> applies the incomplete LU preconditioner.
</li>
<li>
<b>MGMRES_ST</b> applies restarted GMRES to a matrix in sparse triplet form.
</li>
<li>
<b>MULT_GIVENS</b> applies a Givens rotation to two successive entries of a vector.
</li>
<li>
<b>PMGMRES_ILU_CR</b> applies the preconditioned restarted GMRES algorithm.
</li>
<li>
<b>R8VEC_DOT</b> computes the dot product of a pair of R8VEC's.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>REARRANGE_CR</b> sorts a sparse compressed row matrix.
</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 20 December 2011.
</i>
<!-- John Burkardt -->
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