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<a name="Numerical-Integration"></a>
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Next: <a href="Random-Number-Generation.html#Random-Number-Generation" accesskey="n" rel="next">Random Number Generation</a>, Previous: <a href="Fast-Fourier-Transforms.html#Fast-Fourier-Transforms" accesskey="p" rel="previous">Fast Fourier Transforms</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Numerical-Integration-1"></a>
<h2 class="chapter">17 Numerical Integration</h2>
<a name="index-quadrature"></a>
<a name="index-numerical-integration-_0028quadrature_0029"></a>
<a name="index-integration_002c-numerical-_0028quadrature_0029"></a>
<a name="index-QUADPACK"></a>
<p>This chapter describes routines for performing numerical integration
(quadrature) of a function in one dimension. There are routines for
adaptive and non-adaptive integration of general functions, with
specialised routines for specific cases. These include integration over
infinite and semi-infinite ranges, singular integrals, including
logarithmic singularities, computation of Cauchy principal values and
oscillatory integrals. The library reimplements the algorithms used in
<small>QUADPACK</small>, a numerical integration package written by Piessens,
de Doncker-Kapenga, Ueberhuber and Kahaner. Fortran code for <small>QUADPACK</small> is
available on Netlib. Also included are non-adaptive, fixed-order
Gauss-Legendre integration routines with high precision coefficients
by Pavel Holoborodko.
</p>
<p>The functions described in this chapter are declared in the header file
<samp>gsl_integration.h</samp>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">• <a href="Numerical-Integration-Introduction.html#Numerical-Integration-Introduction" accesskey="1">Numerical Integration Introduction</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QNG-non_002dadaptive-Gauss_002dKronrod-integration.html#QNG-non_002dadaptive-Gauss_002dKronrod-integration" accesskey="2">QNG non-adaptive Gauss-Kronrod integration</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QAG-adaptive-integration.html#QAG-adaptive-integration" accesskey="3">QAG adaptive integration</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QAGS-adaptive-integration-with-singularities.html#QAGS-adaptive-integration-with-singularities" accesskey="4">QAGS adaptive integration with singularities</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QAGP-adaptive-integration-with-known-singular-points.html#QAGP-adaptive-integration-with-known-singular-points" accesskey="5">QAGP adaptive integration with known singular points</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QAGI-adaptive-integration-on-infinite-intervals.html#QAGI-adaptive-integration-on-infinite-intervals" accesskey="6">QAGI adaptive integration on infinite intervals</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QAWC-adaptive-integration-for-Cauchy-principal-values.html#QAWC-adaptive-integration-for-Cauchy-principal-values" accesskey="7">QAWC adaptive integration for Cauchy principal values</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QAWS-adaptive-integration-for-singular-functions.html#QAWS-adaptive-integration-for-singular-functions" accesskey="8">QAWS adaptive integration for singular functions</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QAWO-adaptive-integration-for-oscillatory-functions.html#QAWO-adaptive-integration-for-oscillatory-functions" accesskey="9">QAWO adaptive integration for oscillatory functions</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="QAWF-adaptive-integration-for-Fourier-integrals.html#QAWF-adaptive-integration-for-Fourier-integrals">QAWF adaptive integration for Fourier integrals</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="CQUAD-doubly_002dadaptive-integration.html#CQUAD-doubly_002dadaptive-integration">CQUAD doubly-adaptive integration</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="Fixed-order-Gauss_002dLegendre-integration.html#Fixed-order-Gauss_002dLegendre-integration">Fixed order Gauss-Legendre integration</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="Numerical-integration-error-codes.html#Numerical-integration-error-codes">Numerical integration error codes</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="Numerical-integration-examples.html#Numerical-integration-examples">Numerical integration examples</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="Numerical-integration-References-and-Further-Reading.html#Numerical-integration-References-and-Further-Reading">Numerical integration References and Further Reading</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
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Next: <a href="Random-Number-Generation.html#Random-Number-Generation" accesskey="n" rel="next">Random Number Generation</a>, Previous: <a href="Fast-Fourier-Transforms.html#Fast-Fourier-Transforms" accesskey="p" rel="previous">Fast Fourier Transforms</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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