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<html>
<head>
<title>
CHEBYSHEV_INTERP_1D - Chebyshev Polynomial Interpolation in 1D
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
CHEBYSHEV_INTERP_1D <br> Chebyshev Polynomial Interpolation in 1D
</h1>
<hr>
<p>
<b>CHEBYSHEV_INTERP_1D</b>
is a MATLAB library which
determines the combination of Chebyshev polynomials which
interpolates a set of data, so that p(x(i)) = y(i).
</p>
<p>
<b>CHEBYSHEV_INTERP_1D</b> needs the R8LIB library.
The test program needs the TEST_INTERP library.
</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>CHEBYSHEV_INTERP_1D</b> is available in
<a href = "../../c_src/chebyshev_interp_1d/chebyshev_interp_1d.html">a C version</a> and
<a href = "../../cpp_src/chebyshev_interp_1d/chebyshev_interp_1d.html">a C++ version</a> and
<a href = "../../f77_src/chebyshev_interp_1d/chebyshev_interp_1d.html">a FORTRAN77 version</a> and
<a href = "../../f_src/chebyshev_interp_1d/chebyshev_interp_1d.html">a FORTRAN90 version</a> and
<a href = "../../m_src/chebyshev_interp_1d/chebyshev_interp_1d.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/barycentric_interp_1d/barycentric_interp_1d.html">
BARYCENTRIC_INTERP_1D</a>,
a MATLAB library which
defines and evaluates the barycentric Lagrange polynomial p(x)
which interpolates a set of data, so that p(x(i)) = y(i).
The barycentric approach means that very high degree polynomials can
safely be used.
</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
uses divided differences to compute the polynomial interpolant
to a given set of data.
</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/lagrange_interp_1d/lagrange_interp_1d.html">
LAGRANGE_INTERP_1D</a>,
a MATLAB library which
defines and evaluates the Lagrange polynomial p(x)
which interpolates a set of data, so that p(x(i)) = y(i).
</p>
<p>
<a href = "../../m_src/nearest_interp_1d/nearest_interp_1d.html">
NEAREST_INTERP_1D</a>,
a MATLAB library which
interpolates a set of data using a piecewise constant interpolant
defined by the nearest neighbor criterion.
</p>
<p>
<a href = "../../m_src/pwl_interp_1d/pwl_interp_1d.html">
PWL_INTERP_1D</a>,
a MATLAB library which
interpolates a set of data using a piecewise linear interpolant.
</p>
<p>
<a href = "../../m_src/r8lib/r8lib.html">
R8LIB</a>,
a MATLAB library which
contains many utility routines using double precision real (R8) arithmetic.
</p>
<p>
<a href = "../../m_src/rbf_interp_1d/rbf_interp_1d.html">
RBF_INTERP_1D</a>,
a MATLAB library which
defines and evaluates radial basis function (RBF) interpolants to 1D data.
</p>
<p>
<a href = "../../m_src/shepard_interp_1d/shepard_interp_1d.html">
SHEPARD_INTERP_1D</a>,
a MATLAB library which
defines and evaluates Shepard interpolants to 1D data,
which are based on inverse distance weighting.
</p>
<p>
<a href = "../../m_src/spline/spline.html">
SPLINE</a>,
a MATLAB library which
constructs and evaluates spline interpolants and approximants.
</p>
<p>
<a href = "../../m_src/test_interp/test_interp.html">
TEST_INTERP</a>,
a MATLAB library which
defines a number of test problems for interpolation,
provided as a set of (x,y) data.
</p>
<p>
<a href = "../../m_src/test_interp_1d/test_interp_1d.html">
TEST_INTERP_1D</a>,
a MATLAB library which
defines test problems for interpolation of data y(x),
depending on a 2D argument.
</p>
<p>
<a href = "../../m_src/vandermonde_interp_1d/vandermonde_interp_1d.html">
VANDERMONDE_INTERP_1D</a>,
a MATLAB library which
finds a polynomial interpolant to a function of 1D data
by setting up and solving a linear system for the polynomial coefficients,
involving the Vandermonde matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Kendall Atkinson,<br>
An Introduction to Numerical Analysis,<br>
Prentice Hall, 1989,<br>
ISBN: 0471624896,<br>
LC: QA297.A94.1989.
</li>
<li>
Philip Davis,<br>
Interpolation and Approximation,<br>
Dover, 1975,<br>
ISBN: 0-486-62495-1,<br>
LC: QA221.D33
</li>
<li>
David Kahaner, Cleve Moler, Steven Nash,<br>
Numerical Methods and Software,<br>
Prentice Hall, 1989,<br>
ISBN: 0-13-627258-4,<br>
LC: TA345.K34.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "chebyshev_coef_1d.m">chebyshev_coef_1d.m</a>,
determines the coefficients of the Chebyshev interpolant for a set of data.
</li>
<li>
<a href = "chebyshev_interp_1d.m">chebyshev_interp_1d.m</a>,
determines the coefficients of the Chebyshev interpolant for a set of data
and evaluates the interpolant.
</li>
<li>
<a href = "chebyshev_value_1d.m">chebyshev_value_1d.m</a>,
evaluates a Chebyshev interpolant, given its coefficients.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "chebyshev_interp_1d_test.m">chebyshev_interp_1d_test.m</a>, calls all the tests;
</li>
<li>
<a href = "chebyshev_interp_1d_test_output.txt">chebyshev_interp_1d_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "chebyshev_interp_1d_test01.m">chebyshev_interp_1d_test01.m</a>,
plots a piecewise linear interpolant to
the original data, and the Chebyshev interpolant.
</li>
</ul>
</p>
<p>
The program plots a piecewise linear interpolant to
the original data, and the Chebyshev interpolant.
<ul>
<li>
<a href = "p01_data.png">p01_data.png</a>,
a plot of the data and piecewise linear interpolant for problem p01;
</li>
<li>
<a href = "p01_poly.png">p01_poly.png</a>,
a plot of the polynomial interpolant for problem p01;
</li>
<li>
<a href = "p02_data.png">p02_data.png</a>,
a plot of the data and piecewise linear interpolant for problem p02;
</li>
<li>
<a href = "p02_poly.png">p02_poly.png</a>,
a plot of the polynomial interpolant for problem p02;
</li>
<li>
<a href = "p03_data.png">p03_data.png</a>,
a plot of the data and piecewise linear interpolant for problem p03;
</li>
<li>
<a href = "p03_poly.png">p03_poly.png</a>,
a plot of the polynomial interpolant for problem p03;
</li>
<li>
<a href = "p04_data.png">p04_data.png</a>,
a plot of the data and piecewise linear interpolant for problem p04;
</li>
<li>
<a href = "p04_poly.png">p04_poly.png</a>,
a plot of the polynomial interpolant for problem p04;
</li>
<li>
<a href = "p05_data.png">p05_data.png</a>,
a plot of the data and piecewise linear interpolant for problem p05;
</li>
<li>
<a href = "p05_poly.png">p05_poly.png</a>,
a plot of the polynomial interpolant for problem p05;
</li>
<li>
<a href = "p06_data.png">p06_data.png</a>,
a plot of the data and piecewise linear interpolant for problem p06;
</li>
<li>
<a href = "p06_poly.png">p06_poly.png</a>,
a plot of the polynomial interpolant for problem p06;
</li>
<li>
<a href = "p07_data.png">p07_data.png</a>,
a plot of the data and piecewise linear interpolant for problem p07;
</li>
<li>
<a href = "p07_poly.png">p07_poly.png</a>,
a plot of the polynomial interpolant for problem p07;
</li>
<li>
<a href = "p08_data.png">p08_data.png</a>,
a plot of the data and piecewise linear interpolant for problem p08;
</li>
<li>
<a href = "p08_poly.png">p08_poly.png</a>,
a plot of the polynomial interpolant for problem p08;
</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 modified on 16 September 2012.
</i>
<!-- John Burkardt -->
</body>
</html>