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quadrature_golub_welsch.html
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<html>
<head>
<title>
QUADRATURE_GOLUB_WELSCH - Quadrature Points and Weights, Golub Welsch Method
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
QUADRATURE_GOLUB_WELSCH <br> Quadrature Points and Weights, Golub Welsch Method
</h1>
<hr>
<p>
<b>QUADRATURE_GOLUB_WELSCH</b>
is a C++ library which
illustrates the use of the Golub Welsch technique for computing
the points and weights of a Gaussian quadrature rule.
</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>QUADRATURE_GOLUB_WELSCH</b> is available in
<a href = "../../c_src/quadrature_golub_welsch/quadrature_golub_welsch.html">a C version</a> and
<a href = "../../cpp_src/quadrature_golub_welsch/quadrature_golub_welsch.html">a C++ version</a> and
<a href = "../../f77_src/quadrature_golub_welsch/quadrature_golub_welsch.html">a FORTRAN77 version</a> and
<a href = "../../f_src/quadrature_golub_welsch/quadrature_golub_welsch.html">a FORTRAN90 version</a> and
<a href = "../../m_src/quadrature_golub_welsch/quadrature_golub_welsch.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/clenshaw_curtis_rule/clenshaw_curtis_rule.html">
CLENSHAW_CURTIS_RULE</a>,
a C++ program which
defines a Clenshaw Curtis quadrature rule.
</p>
<p>
<a href = "../../cpp_src/quadrature_least_squares/quadrature_least_squares.html">
QUADRATURE_LEAST_SQUARES</a>,
a C++ library which
computes weights for "sub-interpolatory" quadrature rules,
that is, it estimates integrals by integrating a polynomial that
approximates the function data in a least squares sense.
</p>
<p>
<a href = "../../cpp_src/quadrature_weights_vandermonde/quadrature_weights_vandermonde.html">
QUADRATURE_WEIGHTS_VANDERMONDE</a>,
a C++ library which
determines the weights of a quadrature rule using the Vandermonde matrix.
</p>
<p>
<a href = "../../cpp_src/quadrule/quadrule.html">
QUADRULE</a>,
a C++ library which
defines quadrature rules for 1-dimensional domains.
</p>
<p>
<a href = "../../cpp_src/toms655/toms655.html">
TOMS655</a>,
a C++ library which
computes the weights for interpolatory quadrature rule;<br>
this library is commonly called <b>IQPACK</b>;<br>
this is a C version of ACM TOMS algorithm 655.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Philip Davis, Philip Rabinowitz,<br>
Methods of Numerical Integration,<br>
Second Edition,<br>
Dover, 2007,<br>
ISBN: 0486453391,<br>
LC: QA299.3.D28.
</li>
<li>
Sylvan Elhay, Jaroslav Kautsky,<br>
Algorithm 655: IQPACK, FORTRAN Subroutines for the Weights of
Interpolatory Quadrature,<br>
ACM Transactions on Mathematical Software,<br>
Volume 13, Number 4, December 1987, pages 399-415.
</li>
<li>
Jaroslav Kautsky, Sylvan Elhay,<br>
Calculation of the Weights of Interpolatory Quadratures,<br>
Numerische Mathematik,<br>
Volume 40, 1982, pages 407-422.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "qwgw.cpp">qwgw.cpp</a>, the source code.
</li>
<li>
<a href = "qwgw.hpp">qwgw.hpp</a>, the include file.
</li>
<li>
<a href = "qwgw.sh">qwgw.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "qwgw_prb.cpp">qwgw_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "qwgw_prb.sh">qwgw_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "qwgw_prb_output.txt">qwgw_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>IMTQLX</b> diagonalizes a symmetric tridiagonal matrix.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8VEC_EVEN</b> returns an R8VEC of evenly spaced values.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>SGQF</b> computes knots and weights of a Gauss Quadrature formula.
</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 22 February 2014.
</i>
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</body>
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</html>