I understand that the closest (in the Frobenius norm) positive semidefinite matrix can be found via various algorithms such as projection.
Is it possible to find the closest positive definite matrix?
It's an open set so I am thinking that the nearest matrix does not exist. Are there any efficient ways of finding an approximation?
I am guessing you would find the closest positive semidefinite matrix and then permute the diagonal elements slightly to force it to be positive definite.