  In this paper we consider the application of direct methods for solving a
sequence of saddle-point systems. Our goal is to design a method that reuses
information from one factorization and applies it to the next one. In more
detail, when we compute the pivoted $LDL^T$ factorization we speed up
computation by reusing already computed pivots and permutations. We develop our
method in the frame of dynamical systems optimization. Experiments show that
the method improves efficiency over Bunch-Parlett while delivering the same
results.
