(MATLAB) understand quadl vs quadv

Question

Im trying to understand why a call like this

G = const * quadv(fun,a,b,tol)

returns different values than

lenB = length(b)
for  1 = 1:lenB
    G(i) = const .* quadl(fun,a,b,tol)
end

and how to achieve both calls to return the same values ?

EDIT: I would like to run the quadl faster for arrays as well. So I would formulate the above question:

If it is possible, how to call quadl also for arrays (similar like the quadv call above), and thus increase performance by the calculations?

Answer 1

Matlab's quadl uses adaptive Lobatto quadrature; quadv uses adaptive Simpson's rule.

The quality of the answer you get might depend on the function you assume. What does your test fun look like?

I'll assume that you're passing the same function, limits, and tolerance to both calls. That will mean the differences are smaller than the tolerance.

The two methods are different - Gaussian quadrature is not the same as Simpson's rule:

http://en.wikipedia.org/wiki/Gaussian_quadrature