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From Ted Dunning <>
Subject Re: [math] On MATH-995: Problems with LegendreGaussQuadrature class.
Date Fri, 28 Jun 2013 15:32:49 GMT
On Fri, Jun 28, 2013 at 8:14 AM, Gilles <>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 MATH-995. This problem should be observable with any
>> integral,
>> but I observed it with an improper integral. The patch in MATH-995
>> 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:
> 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.]


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"?

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