On Wed, 3 Jul 2013 07:39:00 -0700, Ajo Fod wrote:
I wonder if Clenshaw-Curtis Quadrature (CCQ) is more adapted for
Adaptive
Quadrature than Gauss-Kronrod (GKQ).
As Konstantin already pointed out, the choice of a quadrature rule
is orthogonal to the choice of an adaptive strategy.
It seems like with CCQ the points at
one level of resolution can be reused for the next level.
This is also the purpose of Gauss-Kronrod:
http://en.wikipedia.org/wiki/Gauss–Kronrod_quadrature_formula
The error bounds
for a given level of resolution is the comparable to GKQ, so I'm
guessing
that from an accuracy/evaluation perspective, CCQ is 2 times as
efficient
as GKQ.
According to the Wikipedia article which you site here:
http://en.wikipedia.org/wiki/Clenshaw–Curtis_quadrature
your statement is wrong. [They state that the _weights computation_ is
faster than with Gauss-Kronrod.]
Gilles
Cheers,
Ajo
On Tue, Jul 2, 2013 at 2:09 PM, Gilles <gil...@harfang.homelinux.org>
wrote:
On Tue, 2 Jul 2013 12:54:12 -0400, Konstantin Berlin wrote:
IterateiveLegendreGaussIntegra**tor should be replaced by adaptive
guass-kronrod. The simpson and trapezoidal methods should be
replaced by
their adaptive versions, or at least adaptive wrapper provided for
them.
[I mentioned Gauss-Kronrod very early in the discussion about
MATH-995.]
See also
https://issues.apache.org/**jira/browse/MATH-830<https://issues.apache.org/jira/browse/MATH-830>
Identified sub-tasks can be filed there.
In a library like Commons Math, we aim to provide "low-level" tools
which
knowledgeable users can mix and match to solve a wide range of
problems.
Patches welcome.
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