  We present a class of iterative fully distributed fixed point methods to
solve a system of linear equations, such that each agent in the network holds
one of the equations of the system. Under a generic directed, strongly
connected network, we prove a convergence result analogous to the one for fixed
point methods in the classical, centralized, framework: the proposed method
converges to the solution of the system of linear equations at a linear rate.
We further explicitly quantify the rate in terms of the linear system and the
network parameters. Next, we show that the algorithm provably works under
time-varying directed networks provided that the underlying graph is connected
over bounded iteration intervals, and we establish a linear convergence rate
for this setting as well. A set of numerical results is presented,
demonstrating practical benefits of the method over existing alternatives.
