I need to compute the Cholesky decomposition $A=LL^T$ in order to obtain the matrix $L$.
My matrix $A$ is often badly conditioned (non-positive definite). I am now trying an approach where I normalize $A$ with a matrix $N$ before performing the decomposition. I want to reapply $N$ to the obtained result in order to find the correct matrix $L$.
Is such a method possible, and if so, how and why would it work? Are there any alternative ways to deal with non-positive definite matrices in a Cholesky decomposition?