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<html>
<head>
<title>
TOMS446 - Ten Subroutines for the Manipulation of Chebyshev Series
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS446 <br> Ten Subroutines for the Manipulation of Chebyshev Series
</h1>
<hr>
<p>
<b>TOMS446</b>
is a FORTRAN90 library which
implements ACM TOMS algorithm 446, for the manipulation
of Chebyshev series,
by Roger Broucke.
</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">
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>TOMS446</b> is available in
<a href = "../../c_src/toms446/toms446.html">a C version</a> and
<a href = "../../cpp_src/toms446/toms446.html">a C++ version</a> and
<a href = "../../f77_src/toms446/toms446.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms446/toms446.html">a FORTRAN90 version</a> and
<a href = "../../m_src/toms446/toms446.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/bernstein/bernstein.html">
BERNSTEIN</a>,
a FORTRAN90 library which
evaluates the Bernstein polynomials,
useful for uniform approximation of functions;
</p>
<p>
<a href = "../../f_src/chebyshev/chebyshev.html">
CHEBYSHEV</a>,
a FORTRAN90 library which
computes the Chebyshev interpolant/approximant to a given function
over an interval.
</p>
<p>
<a href = "../../f_src/divdif/divdif.html">
DIVDIF</a>,
a FORTRAN90 library which
computes interpolants by divided differences.
</p>
<p>
<a href = "../../f_src/hermite/hermite.html">
HERMITE</a>,
a FORTRAN90 library which
computes the Hermite interpolant, a polynomial that matches function values
and derivatives.
</p>
<p>
<a href = "../../f_src/pppack/pppack.html">
PPPACK</a>,
a FORTRAN90 library which
computes piecewise polynomial functions, including cubic splines.
</p>
<p>
<a href = "../../f_src/spline/spline.html">
SPLINE</a>,
a FORTRAN90 library which
can construct and evaluate spline interpolants and approximants.
</p>
<p>
<a href = "../../f_src/test_approx/test_approx.html">
TEST_APPROX</a>,
a FORTRAN90 library which
defines test functions for approximation and interpolation.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Original FORTRAN77 version by Roger Broucke;
FORTRAN90 version by John Burkardt.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Roger Broucke,<br>
Algorithm 446:
Ten Subroutines for the Manipulation of Chebyshev Series,<br>
Communications of the ACM,<br>
October 1973, Volume 16, Number 4, pages 254-256.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms446.f90">toms446.f90</a>, the source code.
</li>
<li>
<a href = "toms446.sh">toms446.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms446_prb.f90">toms446_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "toms446_prb.sh">toms446_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "toms446_prb_output.txt">toms446_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>CHEBY</b> carries out the Chebyshev analysis of one or
more functions.
</li>
<li>
<b>MLTPLY</b> multiplies two Chebyshev series.
</li>
<li>
<b>ECHEB</b> evaluates a Chebyshev series at a point.
</li>
<li>
<b>EDCHEB</b> evaluates the derivative of a Chebyshev
series at a point.
</li>
<li>
<b>DFRNT</b> determines the derivative of a Chebyshev series.
</li>
<li>
<b>NTGRT</b> determines the integral of a Chebyshev series.
</li>
<li>
<b>INVERT</b> computes the inverse Chebyshev series.
</li>
<li>
<b>BINOM</b> calculates the binomial expansion series for
the (-1/M) power of a Chebyshev series.
</li>
<li>
<b>XALFA2</b> computes a Chebyshev series raised to the
(-1/M) power.
</li>
<li>
<b>XALFA3</b> computes a Chebyshev series raised to the
(-1/M) power.
</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 14 September 2011.
</i>
<!-- John Burkardt -->
</body>
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</html>