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<title>QNG non-adaptive Gauss-Kronrod integration - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">17.2 QNG non-adaptive Gauss-Kronrod integration</h3>
<p><a name="index-QNG-quadrature-algorithm-1522"></a>
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.
<div class="defun">
— Function: int <b>gsl_integration_qng</b> (<var>const gsl_function * f, double a, double b, double epsabs, double epsrel, double * result, double * abserr, size_t * neval</var>)<var><a name="index-gsl_005fintegration_005fqng-1523"></a></var><br>
<blockquote>
<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 f over (a,b) 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></blockquote></div>
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