Subject: how to "fool" Gauss-Kronrod 21-point rule
From: Edwin Woollett
Date: Thu, 12 Apr 2012 11:22:45 -0700
Robert,
In your paper
http://riso.sourceforge.net/docs/heterogeneous-polytree.pdf
which I found via
http://en.scientificcommons.org/robert_dodier
on page 5, in section 5: Numerical Subtleties,
Integration Algorithm,
you say:
"Integration algorithm. Numerical integrations in
more than one dimensions are difficult. In the current
implementation, multidimensional integrations are reduced
to repeated one-dimensional integrations. The
one-dimensional integrations are carried out by an
adaptive region-splitting algorithm based on a Gauss-
Kronrod 21-point rule. (The code is a translation
of the QAGS algorithm from quadpack, a collection
of quadrature algorithms available from www.-
netlib.org.) The adaptive quadrature algorithm can
be "fooled" if the integrand varies on a scale much
smaller than I/42, where I is the length of the interval
of integration. For this reason, riso tries to find
the smallest effective support of the integrand, as described
under the preceding heading."
I would be interested in some examples which illustrate
this ability to fool quad_qags.
Ted Woollett