In this project we develop improved numerical methods for the study of Causal Fermion Systems. In particular, building on arXiv:2201.06382 [math-ph], we aim to implement a more efficient parametrization of discrete, finite-dimensional minimizers of the action principle of CFS. Concretely, we want to avoid the parametrization of unitaries as exponentials of generators used previously by either a) projecting out the allowed choice of spacetime operators from randomly generated matrices directly or b) implementing a decomposition of unitaries into elementary rotations from the literature. The latter would also allow to study the action principle on Haar randomly generated configurations. If these methods yield a more efficient implementation than previous works, which I strongly expect, then in the second phase of the project we will explore larger examples as well as numerically study the behaviour of minimizers under additional boundedness constraints.