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arXiv · 2001.03968

Distributed Fixed Point Method for Solving Systems of Linear Algebraic Equations

Dusan Jakovetic·Natasa Krejic·Natasa Krklec Jerinkic·Greta Malaspina·Alessandra Micheletti
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Abstract

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.

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Dusan Jakovetic, Natasa Krejic, Natasa Krklec Jerinkic, Greta Malaspina, Alessandra Micheletti. 2020-01-12. Distributed Fixed Point Method for Solving Systems of Linear Algebraic Equations. https://arxiv.org/abs/2001.03968

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