LDLt factorization for full matrices

[RoyiAvital]

@mstewart

If you are looking for exactly diagonal D for an indefinite matrix, it’s a bit worse than unstable. The decomposition you are looking for does not even exist in general for symmetric indefinite A, even with symmetric pivoting.

What about a symmetric matrix with non negative eigen values (Semi Definite / SPSD)?
Will that case have a stable \boldsymbol{L} \boldsymbol{D} \boldsymbol{L}^{T} decomposition?