[Help-gsl] Re: Question regarding integration.

[Rodney Sparapani]

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