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<title>GNU Scientific Library &ndash; Reference Manual: Series Acceleration</title>

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<a name="Series-Acceleration"></a>
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<p>
Next: <a href="Wavelet-Transforms.html#Wavelet-Transforms" accesskey="n" rel="next">Wavelet Transforms</a>, Previous: <a href="Chebyshev-Approximations.html#Chebyshev-Approximations" accesskey="p" rel="previous">Chebyshev Approximations</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Series-Acceleration-1"></a>
<h2 class="chapter">31 Series Acceleration</h2>
<a name="index-acceleration-of-series"></a>
<a name="index-summation_002c-acceleration"></a>
<a name="index-series_002c-acceleration"></a>
<a name="index-u_002dtransform-for-series"></a>
<a name="index-Levin-u_002dtransform"></a>
<a name="index-convergence_002c-accelerating-a-series"></a>

<p>The functions described in this chapter accelerate the convergence of a
series using the Levin <em>u</em>-transform.  This method takes a small number of
terms from the start of a series and uses a systematic approximation to
compute an extrapolated value and an estimate of its error.  The
<em>u</em>-transform works for both convergent and divergent series, including
asymptotic series.
</p>
<p>These functions are declared in the header file <samp>gsl_sum.h</samp>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="Acceleration-functions.html#Acceleration-functions" accesskey="1">Acceleration functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Acceleration-functions-without-error-estimation.html#Acceleration-functions-without-error-estimation" accesskey="2">Acceleration functions without error estimation</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Example-of-accelerating-a-series.html#Example-of-accelerating-a-series" accesskey="3">Example of accelerating a series</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Series-Acceleration-References.html#Series-Acceleration-References" accesskey="4">Series Acceleration References</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>




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