I have computed the Cholesky of a positive semidifinite matrix $\Theta$. However I wish to know the diagonal elements of the inverse of $\Theta^{-1}_{ii}$. Is it possible to do this using the cholesky that I have computed? Or will finding the Eigen values alone (without the orthonormal matrices of a SVD) help this cause.

Are there any other suggestions or alternative decompositions that will aid finding the inverse matrix diagonal?

Edit: I've seen that **random projections** does wonders for inverting matrices. Could something like this be applied here?