  The decentralized solution of linear systems of equations arises as a
subproblem in optimization over networks. Typical examples include the KKT
system corresponding to equality constrained quadratic programs in distributed
optimization algorithms or in active set methods. This note presents a tailored
structure-exploiting decentralized variant of the conjugate gradient method. We
show that the decentralized conjugate gradient method exhibits super-linear
convergence in a finite number of steps. Finally, we illustrate the algorithm's
performance in comparison to the Alternating Direction Method of Multipliers
drawing upon examples from sensor fusion.
