On Sun, 21 Jul 2013 08:04:05 -0700, Ajo Fod wrote:
[...]
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).
I'm afraid that these are counter-examples to your suppositions.
Please have a look at
https://issues.apache.org/jira/browse/MATH-997
For an idea look at :
https://en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature
Look at what, precisely?
Regards,
Gilles
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