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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 MATLAB 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 = "../../m_src/bernstein/bernstein.html">
BERNSTEIN</a>,
a MATLAB library which
evaluates the Bernstein polynomials,
useful for uniform approximation of functions;
</p>
<p>
<a href = "../../m_src/chebyshev/chebyshev.html">
CHEBYSHEV</a>,
a MATLAB library which
computes the Chebyshev interpolant/approximant to a given function
over an interval.
</p>
<p>
<a href = "../../m_src/chebyshev_series/chebyshev_series.html">
CHEBYSHEV_SERIES</a>,
a MATLAB library which
can evaluate a Chebyshev series approximating a function f(x),
while efficiently computing one, two or three derivatives of the
series, which approximate f'(x), f''(x), and f'''(x),
by Manfred Zimmer.
</p>
<p>
<a href = "../../m_src/divdif/divdif.html">
DIVDIF</a>,
a MATLAB library which
computes interpolants by divided differences.
</p>
<p>
<a href = "../../m_src/hermite/hermite.html">
HERMITE</a>,
a MATLAB library which
computes the Hermite interpolant, a polynomial that matches function values
and derivatives.
</p>
<p>
<a href = "../../m_src/spline/spline.html">
SPLINE</a>,
a MATLAB library which
can construct and evaluate spline interpolants and approximants.
</p>
<p>
<a href = "../../m_src/test_approx/test_approx.html">
TEST_APPROX</a>,
a MATLAB library which
defines test functions for approximation and interpolation.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Original FORTRAN77 version by Roger Broucke;
Matlab 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 = "binom.m">binom.m</a>,
calculates the binomial expansion series for
the (-1/M) power of a Chebyshev series.
</li>
<li>
<a href = "cheby.m">cheby.m</a>,
carries out the Chebyshev analysis of one or
more functions.
</li>
<li>
<a href = "dfrnt.m">dfrnt.m</a>,
determines the derivative of a Chebyshev series.
</li>
<li>
<a href = "echeb.m">echeb.m</a>,
evaluates a Chebyshev series at a point.
</li>
<li>
<a href = "edcheb.m">edcheb.m</a>,
evaluates the derivative of a Chebyshev
series at a point.
</li>
<li>
<a href = "invert.m">invert.m</a>,
computes the inverse Chebyshev series.
</li>
<li>
<a href = "mltply.m">mltply.m</a>,
multiplies two Chebyshev series.
</li>
<li>
<a href = "ntgrt.m">ntgrt.m</a>,
determines the integral of a Chebyshev series.
</li>
<li>
<a href = "xalfa2.m">xalfa2.m</a>,
computes a Chebyshev series raised to the
(-1/M) power.
</li>
<li>
<a href = "xalfa3.m">xalfa3.m</a>,
computes a Chebyshev series raised to the
(-1/M) power.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms446_test.m">toms446_test.m</a>,
calls all tests.
</li>
<li>
<a href = "toms446_test01.m">toms446_test01.m</a>,
tests CHEBY, which computes Chebyshev series.
</li>
<li>
<a href = "toms446_test02.m">toms446_test02.m</a>,
tests MULTPLY, which multiplies two Chebyshev series.
</li>
<li>
<a href = "toms446_test03.m">toms446_test03.m</a>,
tests ECHEB, which evaluates a Chebyshev series.
</li>
<li>
<a href = "toms446_test04.m">toms446_test04.m</a>,
tests EDCHEB, which evaluates the derivative of a Chebyshev series.
</li>
<li>
<a href = "toms446_test05.m">toms446_test05.m</a>,
tests DFRNT, which computes the Chebyshev series of a derivative.
</li>
<li>
<a href = "toms446_test06.m">toms446_test06.m</a>,
tests NTGRT, which computes the Chebyshev series of an indefinite integral.
</li>
<li>
<a href = "toms446_test_output.txt">toms446_test_output.txt</a>,
the output from a run of the sample program.
</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 21 September 2011.
</i>
<!-- John Burkardt -->
</body>
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</html>