On Fri, Jun 28, 2013 at 8:14 AM, Gilles <gilles@harfang.homelinux.org>wrote:
> Hello.
>
> The existing LegendreGaussQuadrature class incorrectly assumes that it has
>> converged for functions where the polynomial approximation fails in a
>> small
>> corner of the integral space.
>>
>> This situation is handled much better with the AdaptiveQuadrature class in
>> the path for MATH995. This problem should be observable with any
>> integral,
>> but I observed it with an improper integral. The patch in MATH995
>> transforms the improper integral to a proper one before applying the
>> LegendreGaussQuadrature class (to show how it fails). It also computes the
>> same proper integral with the Adaptive method to show the proper behavior.
>>
>
> Please note that CM aims at providing _standard_ algorithms.[1]
>
> Wikipedia has this general article:
> https://en.wikipedia.org/wiki/**Adaptive_quadrature<https://en.wikipedia.org/wiki/Adaptive_quadrature>
> where it is mentioned that the problem is broken into
> * standard quadrature rules,
> * logic to subdivide the interval and terminate the algorithm.
>
> As I explained in the other post we must aim at flexibility. In this
> case, that would indeed imply a clean separation, as outlined in the
> article referred to above. [This is obviously not the case in your
> "AdaptiveQuadrature" class.]
>
Gilles,
This guy is reporting a problem with LGQ and you seem to jump on him for
coding style.
Isn't the correct response more along the lines of "Hmm.... interesting
discrepancy. Need to check on it"?
