Say I have a fairly big nontrivial covariance matrix (50x50 or bigger) and I would like to generate a bunch of vectors (say, 10000) whose covariance is consistent with this matrix. How would I go about that?
Assume the means of all the result elements are zero, for simplicity's sake. Optimizing the incremental time for each vector generated is more important than optimizing the preparatory caclculations. Also assume I can generate normally distributed variables with no problem.
I'm guessing you could do it by generating a bunch of independent normally distributed variables, then assigning each element in the result vector as a linear combination of the independent variables, but the exact method is escaping me.
A link to a good (and free) paper or description of the method would also be acceptable.