# Efficient Cholesky decomposition of inverse matrix

I want to generate random numbers from a multivariate normal distribution in Matlab. Normally, this is done like:

$w = \overline{w} + \text{chol}(\Sigma) \cdot \vec{l}$

But in my case I don't know $\Sigma$ itself, but only its inverse $B=\Sigma^{-1}$

Is there a way to calculate $chol(B^{-1})$, without calculating $B^{-1}$? If I can get an expression like

$w = \overline{w} + F(B)~\backslash~ \vec{l}$, where \ is a more optimal way to calculate an inverse in Matlab, that would be great.

-
Not sure if this helps but have you referred mvnrnd? –  Inquest Mar 1 '12 at 18:11
mvnrnd takes sigma as second argument, so I'd have to run mvnrnd(mean,inv(B)) which is a pretty expensive calculation. –  Ben Ruijl Mar 1 '12 at 21:58
I'm doing the same thing, but I have been getting funky results. You can take the cholesky decomposition of $\Sigma^{-1}$ and find the upper cholesky decomposition of that and then take the inverse. However, what I am left with is a triangular matrix that can reproduce $\Sigma$, but it isn't the same as $chol(\Sigma)$ –  John Jan 30 '13 at 19:53