Subject: how to "fool" Gauss-Kronrod 21-point rule
From: Robert Dodier
Date: Sun, 15 Apr 2012 22:24:40 -0400
On 4/12/12, Edwin Woollett <woollett at charter.net> wrote:
> 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.
Well, what I meant is that if two functions f and g agree on
the set of points evaluated by QAGS, and differ elsewhere,
then QAGS will return the same estimate for both, although
the integrals might actually differ by any amount you like.
You could construct an example by what points are evaluated
for an easy function such as sin or whatever, and then
construct a spline which goes through those points as well
as some others which you can choose as you wish.
Sorry for the late reply -- I've been on the road.
best
Robert Dodier