* Does anybody know how to use FFT to compute numerical integration?
@ 2007-06-28 3:41 Michael
[not found] ` <46835E39.8060805@yandex.ru>
0 siblings, 1 reply; 2+ messages in thread
From: Michael @ 2007-06-28 3:41 UTC (permalink / raw)
To: help-gsl, gsl-discuss
The FFT used for numerical integral has the problem of non-adaptive sample
points, which is inefficient.
However I have to use it in my 2D integration problem, for the following
reason:
My 2D integration is:
Integrate( F(v) * FourierTransform[g(t)] (v), v from -infinity to
+infinity ).
------------
g(t)'s evaluation is costly. So I plan to fix the parameter for g(t), and
compute the Fourier Transform of g(t) only once, and store in memroy. And
then in calibration loop, I only vary the parameters for F(v). And each time
for each different set of parameters of F(v), I compute the dot-product of
F(v) sample points and the FT[g(t)] sample points to obtain approximation to
the integral.
My question is: how to improve the accuracy of FFT-based integration? I know
it's inefficient, but is there any remedy at least?
Moreover, is there a better adaptive quadature based "smart" integration
method that can help me deal with the above situation efficiently? I am
thinking of doing a cache for the Fourier Transform of g(t), which is
FT[g(t)](v), since adaptive quadature based integration may sample different
point of FT[g(t)](v) each time... but perhaps the overhead introduced in the
cache may outweigh the smart adaptive integration itself...
Any suggestions? Thanks a lot!
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: [Help-gsl] Does anybody know how to use FFT to compute numerical integration?
[not found] ` <468362B4.5070604@yandex.ru>
@ 2007-06-28 11:41 ` Michael
0 siblings, 0 replies; 2+ messages in thread
From: Michael @ 2007-06-28 11:41 UTC (permalink / raw)
To: Evgeny Kurbatov; +Cc: help-gsl, gsl-discuss
No this is not an option. I don't have FT[f](v) available. Thanks!
On 6/28/07, Evgeny Kurbatov <EvgenyKurbatov@yandex.ru> wrote:
>
> Or you can calculate the expression
> Integrate( g(t) * FT[F](t), t )
>
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2007-06-28 3:41 Does anybody know how to use FFT to compute numerical integration? Michael
[not found] ` <46835E39.8060805@yandex.ru>
[not found] ` <468362B4.5070604@yandex.ru>
2007-06-28 11:41 ` [Help-gsl] " Michael
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