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Next: <a href="QAG-adaptive-integration.html#QAG-adaptive-integration" accesskey="n" rel="next">QAG adaptive integration</a>, Previous: <a href="Numerical-Integration-Introduction.html#Numerical-Integration-Introduction" accesskey="p" rel="previous">Numerical Integration Introduction</a>, Up: <a href="Numerical-Integration.html#Numerical-Integration" accesskey="u" rel="up">Numerical Integration</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="QNG-non_002dadaptive-Gauss_002dKronrod-integration-1"></a>
<h3 class="section">17.2 QNG non-adaptive Gauss-Kronrod integration</h3>
<a name="index-QNG-quadrature-algorithm"></a>

<p>The QNG algorithm is a non-adaptive procedure which uses fixed
Gauss-Kronrod-Patterson abscissae to sample the integrand at a maximum of 87
points.  It is provided for fast integration of smooth functions.
</p>
<dl>
<dt><a name="index-gsl_005fintegration_005fqng"></a>Function: <em>int</em> <strong>gsl_integration_qng</strong> <em>(const gsl_function * <var>f</var>, double <var>a</var>, double <var>b</var>, double <var>epsabs</var>, double <var>epsrel</var>, double * <var>result</var>, double * <var>abserr</var>, size_t * <var>neval</var>)</em></dt>
<dd>
<p>This function applies the Gauss-Kronrod 10-point, 21-point, 43-point and
87-point integration rules in succession until an estimate of the
integral of <em>f</em> over <em>(a,b)</em> is achieved within the desired
absolute and relative error limits, <var>epsabs</var> and <var>epsrel</var>.  The
function returns the final approximation, <var>result</var>, an estimate of
the absolute error, <var>abserr</var> and the number of function evaluations
used, <var>neval</var>.  The Gauss-Kronrod rules are designed in such a way
that each rule uses all the results of its predecessors, in order to
minimize the total number of function evaluations.
</p></dd></dl>





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