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We present a class of iterative fully distributed fixed point methods tosolve a system of linear equations, such that each agent in the network holdsone of the equations of the system. Under a generic directed, stronglyconnected network, we prove a convergence result analogous to the one for fixedpoint methods in the classical, centralized, framework: the proposed methodconverges 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 thenetwork parameters. Next, we show that the algorithm provably works undertime-varying directed networks provided that the underlying graph is connectedover bounded iteration intervals, and we establish a linear convergence ratefor this setting as well. A set of numerical results is presented,demonstrating practical benefits of the method over existing alternatives.

Distributed Fixed Point Method for Solving Systems of Linear Algebraic Equations