[Help-gsl] Re:Question regarding integration

[Jigal A]

Sorry for the long delay....

The integration is of an electromagnetic (potential) field (5D) of a point
source.

The numerator is proportional to the (5D) velocity vector of the source
(v_3 = cosh(s), v_0 = sinh(s), v_4 = 1, v_1 = v_2 = 0)

The denominator is 1/R^(3/2) (the 5D green-function of the wave equation)
where
R^2 = x^2 + y^2 + (z - cosh(s))^2 + (tau - s)^2 - (t - sinh(s))^2

I need to integrate all the potential components, namely, the 3 non-zero
components.
The edges where R=0 are regularized separately by hand.
So - basically, the integrals are well defined, and basically, smooth
functions of s.
The denominator is a somewhat involved function, and if it could be shared,
then it would save
a few cycles.

As for Monte Carlo method, I never thought of using non-deterministic
methods such as MC.
I thought that since the integrand is smooth function, I need to pursue more
"exact", or
deterministic methods.

What do you think?
What about integrating this as an ODE? Is that considered numerically good?
(in terms of accuracy, that is).

Best regards,
Jigal.


Is MC slower?
> Can MC handle difficult integrands?
>
>
> 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
> >
> >
> >
> > _______________________________________________
> > Help-gsl mailing list
> > address@hidden
> > http://lists.gnu.org/mailman/listinfo/help-gsl
> >
>
>
>
>