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Viewing changes to Integrands-with-weight-functions.html

Committer: Bazaar Package Importer
Author(s): Dirk Eddelbuettel
Date: 2006-04-12 19:46:32 UTC
mfrom: (1.3.1 upstream) (3.1.1 dapper)
Revision ID: james.westby@ubuntu.com-20060412194632-c9lodpl075pv9si3

Tags: 1.8-1

* New upstream release 1.8
* As with previous releases, the sources were obtained from the FSF web
pages by means of a wget call (c.f. the debian/rules target 'upstream')

* debian/control: Standards-Version increased to 3.6.2
* debian/copyright: Updated FSF address
* debian/rules: Set DH_COMPAT=4

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Integrands-with-weight-functions.html

<head>

<title>Integrands with weight functions - GNU Scientific Library -- Reference Manual</title>

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<p>

Next: <a rel="next" accesskey="n" href="Integrands-with-singular-weight-functions.html#Integrands-with-singular-weight-functions">Integrands with singular weight functions</a>,

Previous: <a rel="previous" accesskey="p" href="Integrands-without-weight-functions.html#Integrands-without-weight-functions">Integrands without weight functions</a>,

Up: <a rel="up" accesskey="u" href="Numerical-Integration-Introduction.html#Numerical-Integration-Introduction">Numerical Integration Introduction</a>

<hr>

</div>

<h4 class="subsection">16.1.2 Integrands with weight functions</h4>

<p><a name="index-Clenshaw_002dCurtis-quadrature-1345"></a><a name="index-Modified-Clenshaw_002dCurtis-quadrature-1346"></a>For integrands with weight functions the algorithms use Clenshaw-Curtis

quadrature rules.

<p>A Clenshaw-Curtis rule begins with an n-th order Chebyshev

polynomial approximation to the integrand. This polynomial can be

integrated exactly to give an approximation to the integral of the

original function. The Chebyshev expansion can be extended to higher

orders to improve the approximation and provide an estimate of the

error.

</body></html>

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