A similar question was asked here, but due to the application an alternative solution was given. But I really do want a Cholesky decomposition of the inverse of a matrix.
To be specific, I want to compute a lower triangular matrix $L$ such that
$\Sigma L L^T = I$
where $\Sigma$ is a given positive semi-definite matrix and $I$ is an identity matrix.
In MATLAB I can achieve this by calling
chol(inv(sigma), 'lower'), but I'd like to avoid inverting a dense matrix if it can be done by inverting a triangular matrix instead.
I know I can do
L = inv(chol(sigma, 'lower')), but then I have
$\Sigma L^T L = I$
which is not what I need.