Re: [Help-gsl] Re: Question regarding integration.

[Michael]

Hi folks,

Have anybody had experience with MC or QMC on 1D integrations?

My trouble is that it is a very complicated complex line integral(by
changing of variable, it is now a real line integral, but the
integrand is complex-valued, and the final integrated result is real),
on infinite interval.

My integrator has to work for all combinations of parameters. So my
integrator met a lot of numerical difficulty if the integrand is not
very well-behaved for some combinations of parameters. There is no
smart way to adapt the integral itself to the changing parameters.
Truncating point is another big headache.

All in all, there is a lot of trouble in numerical integration. I am
very interested in hearing your comments about MC or QMC for 1D
difficult integrations, both in terms speed and accuracy. Thanks a
lot!

>
> On 7/30/07, Rodney Sparapani <address@hidden> wrote:
> > Jigal Aharonovich wrote:
> > > Hi there,
> > >
> > > I need to integrate a vector function of a scalar variable, namely, a
> > > set of functions
> > > parameterized with the same parameter.
> > > All function share a common factor, which is also a function.
> > >
> > > I see the following options:
> > >
> > > 1. Regardless of the common factor, integrate them as separate functions,
> > >    with the quadpack set of the integrators.
> > >    (well, choosing one of the integrators, that is...)
> > >    This pays the penalty of recalculating the factor function for all
> > > integrator instances.
> > >
> > > 2. Integrate them as an ODE set, where there are no mutual dependencies
> > > between them.
> > >    However, in each ODE step, the factor function is computed only once.
> > >
> > > Questions:
> > > 1. What would you recommend?
> > > 2. Pardon my ignorance, but are these methods equivalent, in the
> > > numerical sense?
> > >
> > > Kinds regards,
> > > Jigal.
> >
> > Hi Jigal:
> >
> > Hard to say without knowing what the functions look like.  But, if you
> > can write these as finite expectation integrals, then monte carlo
> > integration would allow for simultaneous sampling and estimation.
> > However, that does not appear to
> > be either 1. or 2. so you may have already eliminated that possibility.
> >
> > Rodney
> >
> >
> >
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> >
>