On Sun, 21 Jul 2013 08:04:05 0700, Ajo Fod wrote:
> The patches for Math994 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 :
> https://en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature
>
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
variables.
The goal would be to create a code similar to
"IterativeGaussLegendreIntegrator"
but with a different adaptive strategy: instead of dividing the
interval
into equallength subintervals, it would... (well, you know).
What do you think?
Gilles

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