  Two new methods have been proposed for solving the gravitational constraints
without using elliptic solvers by formulating them as either an
algebraic-hyperbolic or parabolic-hyperbolic system. Here, we compare these two
methods and present a unified computational infrastructure for their
implementation as numerical evolution codes. An important potential application
of these methods is the prescription of initial data for the simulation of
black holes. This paper is meant to support progress and activity in that
direction.
