[Math] Does any commiter understand Change of variables?

[Ajo Fod <aj...@gmail.com>]

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

Re: [Math] Does any commiter understand Change of variables?

[Ajo Fod <aj...@gmail.com>]

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 <te...@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 <aj...@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
> >
>

Re: [Math] Does any commiter understand Change of variables?

[Ted Dunning <te...@gmail.com>]

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 <aj...@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
>