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From Gilles <>
Subject Re: [math] new feature to allow infinite limits in numerical integration.
Date Sun, 21 Jul 2013 23:57:31 GMT
On Sun, 21 Jul 2013 08:04:05 -0700, Ajo Fod wrote:
> The patches for Math-994 have been reworked ... slightly better 
> design.

Sorry but I don't understand the purpose of adding a patch to
a closed issue...

> Here is some numerical analysis on the issue:
> Laguerre is defined only in [0,+ve Inf]
> Hermite is defined in [-Inf,+Inf]
> I have two issues with the above:
> 1: Cant imagine how someone would use AQ. Which means as Gilles 
> noticed,
> you can't focus on the hard to converge sections of the integral.
> 2: If you use the integration without AQ. Any function that has a 
> high
> frequency region somewhere off the region where the polynomial 
> focuses, the
> integral probably won't converge. For Hermite with its weighting in
> e^(-x^2) ... good luck with convergence with say computing CDF of 
> N(0,100)
> or for that matter N(100,1).
> For an idea look at :

You are again mixing two concepts:
  * improper integrals
  * adaptive quadrature
[We already talked about that long ago.]

Let's be practical: I propose that you focus on adaptive quadrature
_first_ because we know that it is needed (a building block) in order
to perform integration on an infinite interval, using a change of
The goal would be to create a code similar to 
but with a different adaptive strategy: instead of dividing the 
into equal-length sub-intervals, it would... (well, you know).

What do you think?


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