Computing the geometric median
Matlab, 77 75

I just use the definition of the geometric median with a numerical minimization. In this case I make use of the Nelder-Mead simplex algorithm. It sould always converge as we try to find the minimum of a convex function (according to Wikipedia).

n=@(m)trace((m'*m).^.5);f=@(m)fminsearch(@(y)n(bsxfun(@minus,m,y)),m(:,1))


Old version:
    n=@(m)sum(diag(m'*m).^.5);f=@(m)fminsearch(@(y)n(bsxfun(@minus,m,y)),m(:,1))

The input format is a matix with the input vectors as columns, e.g:

m = [[2; 20; 3; 30],[20; 2; 20; 2],[1; 2; 3; 4]];