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<html>
<head>
<title>
TOMS453 - Gaussian Quadrature Formulas for Bromwich's Integral
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS453 <br> Gaussian Quadrature Formulas for Bromwich's Integral
</h1>
<hr>
<p>
<b>TOMS453</b>
is a FORTRAN90 library which
implements ACM TOMS algorithm 453, which computes the abscissas
and weights of a Gaussian quadrature formula of given order for
Bromwich's integral.
</p>
<p>
The Bromwich integral is the inverse of the Laplace transform.
</p>
<p>
While the text of many ACM TOMS algorithms is available online
through ACM:
<a href = "http://www.acm.org/pubs/calgo/">
http://www.acm.org/pubs/calgo</a>
or NETLIB:
<a href = "http://www.netlib.org/toms/index.html">
http://www.netlib.org/toms/index.html</a>, most of the early
algorithms are not available. This is one of them. I typed it
in.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<pre><tt>
call bromin ( n, s, tol, xr, xi, wr, wi, eps, ier )
</tt></pre>
<dl>
<dt>
<b>N</b
</dt>
<dd>
the order of the rule;
</dd>
<dt>
<b>S</b
</dt>
<dd>
the parameter in the integral;
</dd>
<dt>
<b>TOL</b
</dt>
<dd>
an error tolerance;
</dd>
<dt>
<b>XR, XI</b
</dt>
<dd>
the real and imaginary parts of the abscissas;
</dd>
<dt>
<b>WR, WI</b
</dt>
<dd>
the real and imaginary parts of the weights;
</dd>
<dt>
<b>EPS</b
</dt>
<dd>
the relatve accuracy estimate;
</dd>
<dt>
<b>IER</b
</dt>
<dd>
the error flag.
</dd>
</dl>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS453</b> is available in
<a href = "../../f77_src/toms453/toms453.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms453/toms453.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Robert Piessens,<br>
Some Aspects of Gaussian Quadrature Formulas for
the Numerical Inversion of the Laplace Transform,<br>
The Computer Journal,<br>
November 1971, Volume 14, pages 433-435.
</li>
<li>
Robert Piessens,<br>
Algorithm 453: Gaussian Quadrature Formulas for
Bromwich's Integral,<br>
Communications of the ACM,<br>
August 1973, Volume 16, Number 8, pages 486-487.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms453.f90">toms453.f90</a>, the source code.
</li>
<li>
<a href = "toms453.sh">toms453.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms453_prb.f90">toms453_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "toms453_prb.sh">toms453_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "toms453_prb_output.txt">toms453_prb_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BROMIN</b> computes the abscissas and weights for
a Gaussian quadrature formula for Bromwich's integral.
</li>
<li>
<b>DGAMMA</b> calculates the gamma function for a real argument X.
</li>
<li>
<b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 12 July 2008.
</i>
<!-- John Burkardt -->
</body>
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