Distributed Fixed Point Method for Solving Systems of Linear Algebraic Equations

01/12/2020
by   Dusan Jakovetic, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset