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From Ajo Fod <ajo....@gmail.com>
Subject Re: [Math] Does any commiter understand Change of variables?
Date Sat, 20 Jul 2013 18:43:52 GMT
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

I think by now Gilles might have finished his attempt at Gauss-Hermite ...
perhaps he can say what he saw on tests.

That was easier to answer!

Cheers,
Ajo




On Sat, Jul 20, 2013 at 11:11 AM, Ted Dunning <ted.dunning@gmail.com> wrote:

> The math is quite simple.
>
> What is not clear is what the numerical properties are for substitution of
> the sort being advocated.
>
> Which functions will do better with substitution?  Which will do better
> with Laguerre polynomials?
>
>
>
> On Sat, Jul 20, 2013 at 8:59 AM, Ajo Fod <ajo.fod@gmail.com> wrote:
>
> > The method is described here:
> > http://en.wikipedia.org/wiki/Integration_by_substitution
> >
> > My patch uses it for improper integration via the change of variable
> > t/(1-t^2) as suggested in :
> > http://en.wikipedia.org/wiki/Numerical_integration
> >
> > Please reach back if anyone understands this concept.
> >
> > Cheers,
> > -Ajo
> >
>

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