[Numpy-discussion] Numeric integration of higher order integrals

Mario Bettenbuehl bettenbu@uni-potsdam...
Wed Jun 1 04:44:08 CDT 2011

Hello everyone,

I am currently tackling the issue to numerically solve an integral of 
higher dimensions numerically. I am comparing models
and their dimension increase with 2^n order.
Taking a closer look to its projections along the axes, down to a two 
dimensions picture, the projections are of Gaussian nature, thus
they show a Gaussian bump.

I already used to approaches:
     1. brute force:        Process the values at discrete grid points 
and calculate the area of the obtained rectangle, cube, ... with a grid 
of 5x5x5x5 for a 4th order equation.
     2. Gaussian quad:    Cascading Gaussian quadrature given from 
numpy/ scipy with a grid size of 100x100x...

The problem I have:
For 1:    How reliable are the results and does anyone have experience 
with equations whose projections are Gaussian like and solved these with 
the straight-forward-method? But how large should the grid be.
For 2:    How large do I need to choose the grid to still obtain 
reliable results? Is a grid of 10x10 sufficiently large?

Thanks in advance for any reply. If needed, I'll directly provide 
further informations about the problem.

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