On 7/19/13 2:36 PM, Konstantin Berlin wrote:
> The question is how correctly to do AQ and how to correctly handle
>
>> improper integrals. What I would appreciate is some real numerical
>> analysis or pointers to where we can do the research to support what
>> Ajo is asking us to commit. Just running tests on one problem
>> instance demonstrates nothing. I asked politely several times and
>> got no response.
>>
>
> Page 170 of numerical recipes third edition.
>
> "The basic trick for improper integrals is to make a change of variables to
> eliminate the singularity or to map an infinite range of integration to a
> finite one."
>
> See also
> http://www.gnu.org/software/gsl/manual/html_node/QAGIadaptiveintegrationoninfiniteintervals.html#QAGIadaptiveintegrationoninfiniteintervals
>
> I hope this can convince people..
Thanks! This is not really numerical analysis, but it is a start
and an indication that there are at least some standard
implementations that work this way. What would be helpful is some
general references that provide complexity and error analysis and
ideally characterize the functions for which the change of variable
approach is better than GaussHermite, per the first recommendation
in [1]
[1] http://en.wikipedia.org/wiki/Numerical_integration
>

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