inversion of covariance sub-matrices

Hi,

I am having the following problem and was wondering whether anybody
could help.

I have an n x p data matrix X containing n observations on p
variables, which I use to compute the p x p covariance matrix X ' X
and its inverse.

Now, call D ' D the q x q sub-matrix of X ' X obtained by taking q
columns and q rows of X ' X.

I need to efficiently compute the inverse of D ' D for all q=1,
2, ..., p-1, sequentially (i.e. starting with only one variable, and
adding one variable at a time).

Can this be done recursively, or efficiently using the inverse of X '
X?

Thanks,

John


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