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Viewing changes to Integrands-without-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-without-weight-functions.html

<head>

<title>Integrands without weight functions - GNU Scientific Library -- Reference Manual</title>

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<p>

Next: <a rel="next" accesskey="n" href="Integrands-with-weight-functions.html#Integrands-with-weight-functions">Integrands with 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">16.1.1 Integrands without weight functions</h4>

<p><a name="index-Gauss_002dKronrod-quadrature-1344"></a>The algorithms for general functions (without a weight function) are

based on Gauss-Kronrod rules.

<p>A Gauss-Kronrod rule begins with a classical Gaussian quadrature rule of

order m. This is extended with additional points between each of

the abscissae to give a higher order Kronrod rule of order 2m+1.

The Kronrod rule is efficient because it reuses existing function

evaluations from the Gaussian rule.

<p>The higher order Kronrod rule is used as the best approximation to the

integral, and the difference between the two rules is used as an

estimate of the error in the approximation.

</body></html>

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