Matrix decomposition via schur complement


I would like to solve multiple linear systems Ax=b_i via Eigen, wehre A is a block diagonal matrix
A = [M, B; B^T, 0] with M symmetric and positive definite and B has full row rank.
The standard LU is too slow for me. So I thought I could use the shur complement and compute the decomposition of M and B(M^-1)B^T. This works fine and the computation of the required decomposition is faster but I need more time to compute x as multiple solve operations are required.

Is there a good way to compute x with the structure of A in mind?

Are you using a KDE app to do this? If so, which one?

Closing, this has nothing to do with KDE.