Given a positive definite matrix $\Sigma$, how can I compute the Cholesky decomposition of $\Sigma^{-1}$ from the Cholesky decomposition of $\Sigma$?
I know that $\left(L L^T \right)^{-1} = L^{-T}L^{-1}$, but is there a way to directly compute the lower triangular matrix of the Cholesky decomposition of $\Sigma^{-1}$ from $L$?