Distributed fixed point method for solving systems of linear algebraic equations

Dušan Jakovetić, Nataša Krejić, Nataša Krklec Jerinkić, Greta Malaspina, Alessandra Micheletti
2021 Automatica  
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 or several 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
more » ... e rate in terms of the linear system and 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.
doi:10.1016/j.automatica.2021.109924 fatcat:tb22zshwi5gf5ciolnotnc4l3u