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<title>GNU Scientific Library – Reference Manual: Chebyshev Approximation Examples</title>
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<a name="Chebyshev-Approximation-Examples"></a>
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<p>
Next: <a href="Chebyshev-Approximation-References-and-Further-Reading.html#Chebyshev-Approximation-References-and-Further-Reading" accesskey="n" rel="next">Chebyshev Approximation References and Further Reading</a>, Previous: <a href="Derivatives-and-Integrals.html#Derivatives-and-Integrals" accesskey="p" rel="previous">Derivatives and Integrals</a>, Up: <a href="Chebyshev-Approximations.html#Chebyshev-Approximations" accesskey="u" rel="up">Chebyshev Approximations</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Examples-21"></a>
<h3 class="section">29.6 Examples</h3>
<p>The following example program computes Chebyshev approximations to a
step function. This is an extremely difficult approximation to make,
due to the discontinuity, and was chosen as an example where
approximation error is visible. For smooth functions the Chebyshev
approximation converges extremely rapidly and errors would not be
visible.
</p>
<div class="example">
<pre class="verbatim">#include <stdio.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_chebyshev.h>
double
f (double x, void *p)
{
if (x < 0.5)
return 0.25;
else
return 0.75;
}
int
main (void)
{
int i, n = 10000;
gsl_cheb_series *cs = gsl_cheb_alloc (40);
gsl_function F;
F.function = f;
F.params = 0;
gsl_cheb_init (cs, &F, 0.0, 1.0);
for (i = 0; i < n; i++)
{
double x = i / (double)n;
double r10 = gsl_cheb_eval_n (cs, 10, x);
double r40 = gsl_cheb_eval (cs, x);
printf ("%g %g %g %g\n",
x, GSL_FN_EVAL (&F, x), r10, r40);
}
gsl_cheb_free (cs);
return 0;
}
</pre></div>
<p>The output from the program gives the original function, 10-th order
approximation and 40-th order approximation, all sampled at intervals of
0.001 in <em>x</em>.
</p>
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